Yes, you can sue your employer. This is serious and you have damages for this invasion of your privacy. Look for an employment and privacy lawyer in Los Angeles. It's not something we would handle, but other lawyers might.
There are a couple of issues. How did your employer come to find out this medical information? Was it provided to him as part of your employment hiring/certification process/benefits? This is important. If you provided the information to your employer in general conversation or it was provided by a third party, such as one of the other parties involved, then you may not have a cause of action. If, however, the information was disclosed to your employer as a condition of employment or some other employment related activity, then your employer had a duty to keep that information confidential. Not only may your employer have violated your general right to privacy as an employee, but may have also run afoul of the Health Insurance Portability and Accountability Act ("HIPAA") and other laws.
I would document everything and then contact a lawyer. You have to move to protect your rights immediately since the longer this issue is not address, the potential for the information to be spread further grows. You may even want to tell your employer that to immediately stop disclosing and discussing your personal health issues even before you retain an attorney. Of course, you should do it verbally and in writing.
The above response is made for general informational and discussion purposes and does not constitute legal advice and is not intended to create an attorney client relationship. Please consult an attorney about the particulars of your case.