I got banned?

First things first, file a support ticket to get in contact with Riot support. Beware though, it may take a bit of time for them to address your ticket.

You said you haven't played in a few months but you have quite a few games that were recently played in your match history. That alone could mean that your account was compromised and the person that used it was the one committing those offenses.

File that support ticket, try and explain the situation in as much detail as possible, and hopefully you can work something out.