The reason for this might be the type of adc you are playing, might be your current elo, and might be your knowledge of the game.. I suggest picking up lucian. You need far less peel and his mid game is very strong for an adc. Thats part of the difference you are feeling between adc and mid laners.
Mid lane mages are designed to have a strong mid game bc their dmg can come simply from maxing an ability and getting that base dmg up. Also their boots help a bit more imo. So they are pretty well set up after winning lane bc they already have a strong mid game and getting fed makes it that much stronger.
Adc's get fed in lane and then that just makes them very relevant in the mid game, but less so than a mage that is only fed from farm. However, if there is a fed dive champion on the enemy team then you are useless (I think you know what I am talking about).
Lucian is an adc that is like a mage bc his q has great base dmg and even better scaling. He also is difficult to dive, so you can eliminate some of that frustration at having won lane and then feeling useless bc fed renekton. Additionally, it is also less awkward to build last whisper second on him (its the same with draven and Graves).
Also, you might want to start thinking about if you REALLY need to be part of that teamfight going on in mid lane or if farming might help you toward your third item which is where you actually start being a frigging ad carry.
