I talked to another girl who went to human resources because her ex also at work was annoying her. And they told her as long as there's no harassment or threats they can't do anything about "gossiping" - people are going to be people and talk.
Most Helpful Girl
It is harrassment as people are now treating you differently. Do some research on workplace harrassment and bullying:
Most Helpful Guy
I will assume that this is a job that you don't want to leave. Obviously, the easiest solution is to find another job (and that is the absolute best solution) but I do understand that some jobs cannot be easily replaced.
She is apparently spreading rumors about you. Have you done anything for which others would judge you harshly? If you want to stay and you want to combat the rumors, I see three ways you can do this.
1. Go to her and confront her about spreading rumors. Tell her that if it doesn't stop immediately, you will "fight fire with fire" and drop a few hints to people about her indiscretions. . . and you promise that the things you say will be as truthful as the things she has said.
2. Start spreading rumors about you. If you do this directly, it will appear that you are just trying to get revenge on her, so you will need to enlist the aid of a trusted friend. Tell the friend that you want him to discreetly let a few other people know - the known gossip mongers - that you caught her cheating with a co-worker. Don't reveal the name of the co-worker. When the others ask your friend who her other partner was, have him say, "He wouldn't even tell me if it was another guy or a girl."
This is clearly an extremely dirty tactic and I don't give this my highest recommendation on the basis of ethics and morality, but it may be effective.
3. Go to your immediate supervisor and discuss the problem with him or her. Let your boss know that the girl was cheating on you, got very angry about being caught, and you suspect that she is spreading lies about you. Your boss will probably talk to her boss and the word will probably get around about what happened.
This situation is a poster child for the rule about not dating co-workers. Experience is a harsh mistress and this is a very difficult way to learn a lesson, so I hope you will learn it well.