Banned For cheating even though i didnt cheat

I was playing csgo with some friends until i got bored and decided to try to play some league. Everytime i tried to login it will bring me into the client but into a game but it would say failed to reach due to connection. So i tried over and over again, so i finally asked one of my friends to check and see if someone was playing on that account. And what do you know there is someone playing on it, ranked too. So I immediately went to go change my password so this person will not be able to log into my account. When i finally changed it, I was put into a game so I decided to play it out since it was a ranked game and i didnt wanna let these people down!(we lost lol). I then signed out of my account and went to play a different game. I then came back to find my account was banned due to third party software. I have never cheated or even thought of cheating in this game, ive been playing this game for roughly four years now and spent well over 1000 dollars in it. I really dont wanna lose my only account that i play on. Im hoping there is away for riot to see where my account was logged in from,because that can easily show you that it wasnt me,because ive only logged in from two places either my own house or whenever i was at a friends house for a lan party,which they are all in the same city. Im really just making this to try and get some help with my account and see if some other people have had similar problems like me. I just really dont wanna lose this account and wanna see if I can get a rioter or someone higher up to see this.