You’re not being irrational in my opinion. Betrayal is a real and valid emotion. It’s also an intense emotion. You’re justified in giving yourself space and being upset. She definitely made a mistake. I think she probably needs to know what she did. She clearly doesn’t see the issue. Not having bipolar makes it very difficult to understand how PERSONAL bipolar disorder can be. If I were in your shoes, I’d say something along the lines of, “I get it may not seem like a big deal, but I’m haveing a REALLY hard time dealing with the fact that you told [so-and-so] something that’s so personal and sensitive to me. I’m not mad, it just hurt me. But I know you didn’t mean to upset me, and I will get over it. I’m working on it.”
Maybe that will provide some needed openness and start some productive and supportive communication. Also, I bet you NEED to get it off your chest. You’d likely feel much better and be able to sincerely forgive her.

Hopefully your coworker keeps it under wraps. *Hugs*