I don't really think there's anything wrong with your champion picks necessarily, and while I can't really vouch for the problems or mistakes you might be making from game to game that might have helped you carry the game properly since I haven't seen your gameplay, but if I'm assuming correctly (you're Level 21, I'm not sure if you've started just recently or if it's a smurf account), it could just be that you lack the necessary experience (and thus game knowledge) to consistently carry when there are so many variables that you are likely not aware of or haven't considered. Here, I'll provide a baseline of things you want to think about when trying to carry a game:
(1) Are you prioritizing** objectives **over kills? If you are using kills as a means to an end in order to gain a gold advantage, create pressure by pushing towers, and secure buffs/dragons/Baron rather than assuming that "I got kills, therefore I should be able to win now that I'm fed", then you have the right mentality. If not, I recommend shifting to become a more objective-focused player rather than purely focusing on "getting fed".
(2) Prioritize consistently high _farm _(100 CS at 10 minutes the ideal baseline for solo lanes and bot lane; 85 CS the benchmark considering the other variables) when determining whether you are "winning" the laning phase or not.
(3) Once you have an advantage (in farm, kills, towers, whatever it happens to be), press it as hard as possible. As an ADC/Marksman, your map movement should be restricted to pushing with your support (or splitpushing alone if you are fed enough and playing a champion like Caitlyn, Corki, Vayne, Sivir, Lucian, etc. that has some mobility and 1v1 outplay potential) in a lane [not necessarily botlane, just an open lane where you are looking to create pressure], grouping for objectives (take towers with team, dragon control, small skirmishes that you need to rotate to), and in general just finding a way to convert your gold/damage advantage into map pressure.
(4) ADC/Marksman, as well as midlane, is the most mechanically-demanding role to play, so make sure that improving your mechanics, last-hitting, and overall micro-play (APM, DI, Stutter-Step/Orb-Walk/Kiting ability, animation-canceling, etc. If you're not familiar already with these terms, go do some research on the side to educate yourself. Use the Internet as a resource to help you improve rather than relying on personal experience for your only source of information.) is an objective in every game. Work on knowing your own damage output limits, your cooldowns, and of course, follow the rule of thumb: "Know thy enemy, know thyself." The better understanding you have of the enemy champions, their capabilities [cooldowns, item and level power spikes, etc.], and the players behind them, the easier it will be to consistently take advantage of them.