What can I do if my coworkers accuse me of mood swings?

If this is a concern of a few coworkers, make sure it is not something they see but you don't admit to.  Employers can "suggest" or something "stipulate" in continued employment with them  for you to go to their Employment Assistance Provider (EAP) if they have noticed the same behavior and concerned of how it is effecting productivity or employee relationships.  No one wants to work in a environment which they consider hostile.  Employers can be held responsible if they do not take action.

Couple of things you can do...

Ask a coworker in which you trust and respect if what others are saying is true?

Seek professional help from your primary care provider or counselor if mood swings do exist.     

I can’t give you legal advice, but employers can suggest you see someone if your behavior is affecting your job. I believe most government agencies have an Employee Assistance Program (EAP) where employees can talk to a therapist about any issue, not just work-related, for free (up to a certain amount of sessions).

I’m wondering, though, why your coworkers would tell your boss this if it’s not true. Is it possible that you're not aware of how your interactions are affecting others? Maybe this “forced counseling” can be an opportunity for some introspection on your part.