Farm Farm and Farm sum mo.....
you gotta be assertive and greedy like most adcs mains are when it comes to cs. Don't be afraid to even take a camp or two from you jungler as long as it is not a important camp like gromp(if you have a tank jungler) red/blue buffs (unless your jungler wants you to have it) and raptors. You cant be passive or nice. If you see minion waves in the side lanes or mid lane unattended and someone is going to clean that up tell then to go somewhere else and you take it. Also don't be afraid to push the side lanes as long as you have proper vision and map awareness. you gotta get as much farm as possible. A greedy adc towards farm is going to be a rich adc that will reek havoc in teamfights.
however.... in Teamfights....
If nobody is peeling for you like in the example you say that the vlad gets to you and kills you or takes you out of the fight everytime, you need tell that fatazz tank Sion to stop diving 30 meters past the enemy teams frontline and get that bloodsucker off of you. The supports #1 job is to peel for you if they didn't initiate the fight. so tell your blitz that if he doesn't initiate the fight with a pull he needs to use his abilitys to peel for you. and remember don't go overboard you need to survive teamfights to keep dealing damage. Hit what is front of you aka they're front-line. don't worry about they're back-line if they are stupid enough to try to walk past your front-line to get to you then focus them.
looking at that teamcomp....
I am just learning about team compositions (so let me know if I am wrong in my analysis) it appears that the opposing team is running a very engage heavy team composition with a little poke mixed in(twisted fate) they have way more lockdown than your team. Your team looks more like a pick composition meant for picking people off before teamfights (ex: warrick and blitz) if you aren't winning the vision war or the enemy team is playing smart and sticking together and not putting the carries in a position to get picked off. your going to be at a disadvantage in a straight up teamfight unless someone on your team is massively fed.
so if your teamcomp is at a disadvantage and they still refuse to peel for you......
splitpush endlessly or play defensively (depending on your adc)
in that situation I would just buy a 
and splitpush relentlessly. ping where you want your support to ward or ward it yourself. I would just make sure i know where twisted fate and the enemy team is at all times. However if that team is smart they would just bait baron pick off and kill warwick and then start it up because your team would already be at a huge teamfight disadvantage because you and Azir (i assume) would be the only main damage dealers with that team comp.
Never be afraid to splitpush as an adc as long as you are smart about it. it forces the enemy team to send someone to deal with you if they know you are skilled enough or fed enough they will have to send more than one person to deal with you. this could possibly weaken they're teamfight and splits the team up witch could create pick opportunity for blitz and warwick. if your still not confident your team is competent enough just tell them to play defensively.
if someone on your team is split-pushing tell your team to play defensive and just waveclear unless you see a possible advantage and can win a fight without your splitpusher.
TLDR version
1 be a greedy adc towards farm and take jungle creeps if possible
2. analyze teamcomps and adjust your adc play to them and try to analyze how they are going to play the comp against you.
3. position well and remind your front-line to always peel for you
4. if they still don't peel and you are losing every fight forget about your team and splitpush
5. if you don't ant to split ask someone else capable of splitpushing to split and focus on farming and turtling and waiting for the enemy team to make a mistake.
(keep in mind that i am a silver 5 support main that has only been playing for 6 months but, I am trying to learn the adc role as well and I am always trying to up my game knowledge.)
. The laning phase went pretty well for me although i died a 2 times to ganks. The problem is not this though. When teamfights started, the enemy 
always chased me and none of my teammates were there to protect me from him. Although sometimes I managed to kill him myself, he always left me with very little HP so i couldn't rejoin the fight. We lost every single teamfight. Team comps were as the following :
Enemy team : 
Sorry if I've done something wrong, it's my first time posting in the boards.
but it already ended before i could get it. I was like 100g away.
,
(no enchantment on this)
Jarvan could tank better than my entire frontline could... That forced blitz to go in the frontline and try to do something leaving me and vlad in a 1v1.
