Could someone give me tips on how to deal with this annoying champion? Constantly having to last it under tower is not really fun, I played Syndra to try to just throw his turrents away but he just makes more to replace them. Then if you ever try to fight him you die from the the rapid fire of all 3 turrents focusing you and those beam attacks hurt a lot.
Depends on if you face him top or mid as to what his worst match ups are. Part of it is knowing the champ you're playing though. For instance 
is a REALLY bad match up for 
so if you're losing it, then it is probably bc you don't know how to play to her strengths against him well. What you want to do is grab his turret, throw it onto another turret and then hit them both to kill them both, you can wipe out his turrets faster than he drops them if you focus on it until he gets 40% cdr. Don't just throw them to different places, kill them.
Anyway, I'll give you a run down of his bad match ups and why I hate to play them (I main donger):
Champs that play top AND mid lane:
, Oh god I hate this champ. His pool let's him avoid dying in your turrets and get out when you expect him to die, and when he starts to get some levels in q and drop the CD of it then he can kill turrets for free pretty much w/ transfusion bc he will sustain back the damage they deal when he q's them with revolver. He basically removes your damage as Heim while sustaining back the damage you do. Horrible match up.
His skittles do bonus damage if they hit a single target so Heimer has to put turrets in the minion wave or you clear them easy. If they are in the wave then you kill turrets while spamming skittles on the wave to push back against the Heimer push. Also in team fights you do aoe which kills his turrets while you're still focusing on champs instead of turrets.
His sustain makes it hard to poke him down, and his silence can destroy a mage, plus it pushes really well with a few levels. If you clear the wave and hit a turret or two w/ silence then suddenly Heim is spending kits to just keep up w/ your push rather than being able to push you under tower and stack up kits for if he wants to rotate or dive. Also Heim is slow so it's easier to hit rupture, and your feast cancels out his ult Q if he tries to use it to 1v2 against your gank, or if he tries to use it to dive you.
Can push the minion wave well and hit your turrets w/ the splash if she lines it up right. Also her ult can save her in your turrets and if she gets you out of them she has so much CC Heim can't escape. Poke down turrets while clearing wave, and be careful w/ ult use.
His laning doesn't crush Heimer, but FUCK this champion. His windwall negates 2 of Heimer's 3 ults, and if it's positioned right in a team fight can block most of the damage from his ult q even (although it's much stronger against ult w or ult e since it just eats them and they're gone).
Aren't the worst match ups, but they are easier to win against Heimer than most.
Top only:
If she gets ahead Heimer is screwed. Her dash can one shot his turrets if she's even when she buys a sheen, and since it resets if it gets a kill, she can dash from one to the next and wipe out a full set of turrets leaving Heim nothing to defend himself. She also scales pretty well.
So much salt. His scream displaces your turrets so he just kicks them back and makes it hard to farm and hard to push. Most important here though is that he can go tp/smite top and have the smite to kill an extra turret and get super tanky w/ the % hp scaling. Also his scream displaces your freaking turrets.... including ult Q. Makes it so if Heimer tries to use ult q it just gets kicked away. Not as strong a removal as just eating it as cho, but also a basic ability instead of an ult.
If he gets ahead at all his spin can remove turrets, also he has some innate sustain even before getting life steal, so he can deal w/ poke somewhat, or take some damage to remove a turret or two. Biggest thing is that Heim is slow, and relies on killing people who dive him in his turrets before they can kill him. You can see where this is going. Honeybadger don't give a shit, he dives Heimer, kills him, then walks away w/ his ult going and a good laugh.
Mid:
Syndra's the only one that is really horrible IMO, but 
and 
can be pretty bad. The first can auto turrets from outside their range and q them when they get low, and she also has the burst to insta kill Heim once she clears turrets. The second can clear turrets safely w/ his soldiers once he gets a few levels and has more CC and mobility than Heim, so once he beats down turrets w/ soldiers it sets up easy ganks.
OTHER:
So the biggest thing is playing something you're comfortable on and better than the Heimer is. The ones above, especially and are painful even when they are average skill level if they play the match up right, but I want to throw out some options for stuff that is balanced vs Heimer, since if you're good on these they may be a better choice for you than the stuff above.
Bursts down Heimer well, but he can block charm w/ his q. Her orb gets to where it can clear turrets, but takes a bit of AP to get ahead.
Can clear waves fast after 6, is hard to burst down w/ egg, wall to stop Heim who has no escapes, and if he groups turrets too close together ult can kill multiple turrets at once. Just have to make it to level 6.
Bad early lane for Fizz, but at 6 he can burst down a Heimer (especially if Heimer doesn't take exhaust), and the stupid gold fish roams SOOOO much better than Heimer. You're really just looking to gank a side lane that is pushed and get a free kill or two and come back to lane w/ enough damage to 1 shot Heim and troll pole out.
Kinda the same as Fizz, rough early w/ the melee, but if Heim doesn't take exhaust he's an easy kill at 6. Also shroud let's you drop turret aggro if the Heim doesn't pink fast enough.
His q is aoe in team fights so it can kill turrets as a side bonus to killing whatever champ you're chasing, and he gets tanky and has good AOE engage, all of which can mess w/ Heim if you survive lane. Since smite is popular on him too right now it gives you a tool to clear turrets or reduce heimer damage when you engage on him.
Good damage, can fang turrets that get poisoned, and can spam fang heimer down easy if he gets poisoned bc he is generally slow at running away.
Her ranged auto is pretty good at clearing turrets if you don't take too much poke while doing it, and her ult can make diving Heimer much more manageable.
Not the best match up for LB, but w/ distortion she can avoid getting hit while poking usually, and if she gets ahead she bursts the squishy dinger down.
People like him as a counter pick, but I'm not convinced. His pool can kill multiple turrets if not spaced right, and his bouncy nightmare bs is great if he gets ahead, but otherwise it can be weaker against Heim than most since if Heim gets enough AP that his turrets survive it, then it doesn't keep jumping and pushing minions. If he's ahead though it bounces through turrets and screws up Heimer.
Alpha strike can dodge grenade stun and wipe out turrets if there aren't minions to bounce to.
Shield to stop poke, pool can kill multiple turrets if Heim isn't good enough to space them right.
Spear the turrets and out sustain him w/ heal, solid burst if you clear out his defenses, plus roams w/ the mobility.
Not a great match up but if you can get a kill early or he doesn't take exhaust snowballing this can be scary.
Good wave clear and range, can poke at turrets if you have the mana for it. Tons of damage and some CC if you have a tanky jungle who can survive the gank and lock Heim down for you.
Pushes as well as Heim, clears multiple turrets easy if you line up your laser right. Massive burst if you catch heimer out.
Poke and wave clear. You don't have an amazing match up, but don't have a bad one. Definitely a solid option if you're good w/ him.
Same as xerath, don't pick him as a "counter" but the match up is decent and makes a good farm fest. If you're good you might even get a kill or two before team fights start, and you have better chase and can bring more damage to team fights if they are mobile and not only in one spot where heimer can put all his turrets.
Hope that was helpful and not too much info. Remember, play what you're best at and think about the ways I described playing stuff above, and you should be able to come out on top if the Heimer isn't better than you. (Remember, he shits on Melee match ups early on so be careful w/ that. God I love Heimer top vs Fiora/Garen/Darius or something. Not as much opportunity to roam from top so you ain't catching up from the side lanes are ya now?)
and profit. Or 
and profit. You can out harass him, just avoid his turrets and then All In him when jungle comes.
pick smite for laning
karthus....
Constantly having to last it under tower is not really fun
That works though... he can't really deny you since the turrets auto shove unless you are bad at farming under tower.
Heimer's turret generation is pretty slow early game. Early game you can just eliminate them as soon as he makes them and he's vulnerable for a while.
Don't allow him to stack turrets in your lane before minions spawn. Destroy them and recall before 1:20 if needed.
Heimer will start to outscale though... His turret generation ramps up significantly as he ranks up his Q.
