Um, Tristana's amazing dude. Her super early game damage is off the charts when you land on someone with her W, she's a devastating lane pusher, she farms crazy cs, and she has nearly the mobility of Ezreal while being a far more powerful endgame carry.
Plus her skill ceiling is very low compared to other carries, like Corki or something.
Maybe you weren't leveling up her W first/ building wrong/ not pushing like a crazy person all game while farming 400+ cs?
I mean you said you've used her a lot, but then you said because she was free, which would lead me to believe you've only played her for a maximum of 7 days at a time, which is like barely touching the tip of the iceberg for mastering a champion and figuring out their full potential. Unless you're playing Sona or something. Huehue.