Man I'm sorry to hear that. was hoping your bosses would give you the benefit of the doubt. I once had a female co-worker accuse me of harrassment with no proof but since I'd been there a while, my bosses told her to fuck off and moved her to another department away from me.
Another guy wasn't so lucky. He turned down a girl cus he's married and the girl accused him of sexual harrassment, got her cousin who worked there to cosign. He got canned. No evidence required, just based on the word of some evil bitch. Unfortunately theres almost nothing we as men can do in those situations short of recording every single moment.
You can however talk to some lawyers see if there is one willing to take up the case for you. It sucks I know but you'll be fine. Chin up.