Okay, from what i can see so far you are actually doing quite well with lux and jax seems fairly average too, but can't say the same for everything else.
From the picks alone, i can assume that you probably have issues with the teamcompositions you get. Communication, teamplay, set ups, chases and traps, lategame etc. Judging by the fact that lux and Annie have your highest winrates for midlaners, and lux prevailing as the only one above 40%, i would say you make best scores with her because you can best make set ups for your team with her. Long range cc, very reliable AoE burst, an last Resort shield.
So, assuming this is the case, (note this is an assumption, so everything from here on is pure hypothesis) you will do best with champions that focus on high AoE and zoning, like lux as mentioned. She is safe, she is always useful, and she is reliable. My advice is stick to her, be a lux main and tilt the ever living Jesus out of your enemies with her laugh.
NOW! since you won't always get midlane, we Need to give you something to do well on the other places too, right? As for toplane you can try sticking to Jax but then be very careful on your matchups. If you have a darius fiora or a malphite in toplane you best make sure you get lots of ganks, if you are jungling then i advice you to Play something that is safe, good clears and not all that hard to Play. you could go with jax again, but then you would Need to actively gank. an alternative is Maokai. He has very strong sustain, and survivability, and his new E makes clearing a lot easier, so you can farm up to lvl 6 and proceed with mad lane-wide ganks for whoever you wanna see burn in hellfire. BUT we all know our lord and saviour autofill, so it is inevitable that you will end up being adc and support once in a while. my suggestions for the start are ezreal and nami.
Ezreal is a very safe adc, skillshot reliant yes but he has massive ranges for a bot lane champ and a free flash on a basic ability. Nami is all about management, where to land your Q, who to slow, who to heal, how to set up your heal for max Efficiency (aka bounces) and in my personal experience nami is one of the easier defensive supports to Play.
Back to lux, if it does not hurt, i would love to know the masteries and runes you take, because even thought many high elo have their recommendations, i personally found that in the end it all depends on playstyle, so if you are to become a lux main you should be prepared, and for your setup ill gladly assist more. i have a runepage which i use on ryze and lux and i have seen very high success with it so far