First of all, I'm only in Gold, so don't get too excited :)
Voluugi13 had a good tip; you should look to get tanky AP items in general; I always go RoA first item and you should almost always build hourglass second or third. Don't be afraid to delay RoA to get resistances if you need them, though. Spirit Visage combos wonderfully with your ult, but it's not an every game purchase.
When it comes to playing, I'll break down each part.
Early game:
Realize your power spike is mid-game and don't always try to win 1v1 against your opponent. Swain is a GREAT gank partner, since he brings lots of cc and dmg. Let your opponent push if you jung can help you. Just try to farm, and harass if you can safely. Swain can be a huge lane bully against melee opponents, but don't get too deep. Many of them are assassins that you mentioned already, and can wreck you if you get low trading.
Mid game:
Pretty typical, just realize that you have power here. Encourage your team to push for objectives, and figure out what your role in the comp needs to be. If your adc is good (and ahead), you might consider sitting on them and peeling. Your dmg with the adc's damage is impeccable.
If your adc has enough peel (or if no one is going to dive them), consider diving yourself. Hourglass will help you with this. You need enough dmg to kill the enemy adc for this to be effective, but it's GREAT if you can get away with it.
Late game:
Swain is great at catching people. Teamfights become more difficult as other player's damage catches up to you. Don't try to be the raid boss and dive 1v5; even if you could do that in the mid game, you likely can't now. Play safe, and watch for getting bursted. That's your weakness.
Place wards (as any champ should) and don't go anywhere alone! Watch for opportunities to catch ppl with your cc and your team can help you burst them.
Hope that helps! Got kind of long; sry.
TL;DR: Swain is not a laning champ! Get your items and play for the mid game. Be careful again late as the enemy catches up.
has waaay too much counters, and way too much ways to be killed early and so get rekt late game. Simply because the best spell to take early (in my opinion) is Nevermore (the root). But the slight.. Ok big ass problem is that Nevermore is easy as hell to dodge. You can simply move around and never get hit my Swain early game, + if you got high mobility he wont be able to land the Decrepify or the Torment, because of their low range (wich is dumb considering the fact that Nevermore has more range you have to get close to actually hit him in it so he got the time to get out). So yea most of the champs in the game can easily take an advantage over him early, and so get fed after. Yes he's is really fun to play but also really easy to lose with. Some of you will say "Baaah u suck thats all"...Well when u look at the facts it's true that Nevermore should have equal range with the others. When it is kinda true that im bad Swain since it's kinda hard to play well, another problem is nearly ALL the easy champs counter him easily. Like Annie
(kind of op dmg imo but mehh) can easily get him with the fact of the high dmg and run and hit. Any assassin
,
,
, etc. can just "teleport" up to him and since he's squichy as hell, when u don't got ult well...#DeathJustRektYou. Nidalee
can VERY easily kill you cause she has high as hell mobility, and Swain is slow so most of the lances hits. adn wayyyy more! Ex: Yasuo the knock up from long distance and the shield gets you dead in a second (knock up then combo and you're dead no way to get out of it). So yea still way more of them these were the worst i've encountered so far.
levels of mobility, you need to improve because that means you have been spoiled by mobility.
