Sole can ban people in here for the slightest of reasons.

OP, you did cheat. However by the sounds of it, it was a genuine mistake. Try to imagine what it would feel like to have someone cheat on you. You found out he humped someone else, and you fought over it. Multiply that and you will get an idea of what he felt.

If you dent someones trust, it can be hard to rebuild, if not impossible. You just have to accept that. Like the others have said, you need to move one. Try to learn from your mistakes though. Betrayal hurts. Judging from your OP, you should have a fair idea of this.

Chalk it upto youthful shenanigans and move on.