I was playing ashe and I went more or less the standard ashe build. Dorans blade>lvl1 boots>rushed infinity edge>lvl 2 boots>brutaliser>emblem of valour>yommuu>starks fervour. was about to build banshee veil but everytime a team fight started I was stun locked so banshees wouldn't made a difference I feel, so I build a last whisper. My thinking behind it was they will stun lock any chance I got so the time I wasn't being stun locked I wanted to do as much damage as possible before i died.
Part of the problem I can see with your build (and something I see on large numbers of AD carries) is that you've built entirely glass cannon. If your team is good enough then there can be reason to do this, but typically when I play Caitlyn I rush Bloodthirster/IE (depends how farmed/fed I am) and then I immediately build Banshees. You said that you were stun locked for a fight but this could be because you DON'T have banshees. Being able to negate the first stun/slow/whatever can mean you being able to flash away and then join the fight when their carry is down.
The other thing is you don't seem to build Attack Speed until really late. I'd consider building Phantom Dancer before Youmous. PD is so good on Ranged AD carries as you literally shred your target in no time at all if you're at 1.5-2 attacks per second range.
Finally, if you're getting picked in team fights, you're more than likely out of position. You have superior range over nearly everyone in the game so you should be poking/kiting from the back and not be in the middle of your team, unless you're fearful of the gank from behind.