Your ex sounds horrendous. They definitely could be spreading rumours about you if they are the type to physically hurt you. These types of people are incredibly frustrating because they will lie and manipulate people to get what they want.

In my experience their poor behaviour does have consequences. It will only be a matter of time before they hurt someone else or get caught up in the lies.

My advice is to tell the truth to people you trust. Try and stay away from your ex because they sound like a dangerous person. Participate in queer community and show them who you are, if you are a kind and considerate person im sure the rumours will quickly be dispelled.