As I read your facts, your confidentiality was breached by the discovery of your pills by your mom.
In all events, your depression and anxiety clearly pre-dated the discussion between your mother and the doctor. You didn't move out because of what the doctor said; you may have moved out because your mom discovered your pills and was strident with you about her views on that issue.
Your issues are not really with your former physician. Seek another physician; take responsibility for your role in what your mother knows about your medical and mental health care; and move forward with the real issues that are underlying your depression and anxiety. Projecting your problems onto your former health care provider will not serve your recovery or your efforts to obtain and retain effective care.
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Typically the mere fact that he discussed something with your mother doesn't necessarilly give a right to sue. Any provider is permitted to disclose to an individual involved in the care of another information that they feel is appropriate, there is a great deal of discretion about this. In this case, it is unfortunate that your mother fooled your psychiatrist into disclosing this information, by making him think that she was mroe involved in your care than she evidently was.
Still, you are in California, and I am not licensed there. It is possible that there are different rules, so if you have a question, you can see a local attorney.
I am licensed in New Mexico and Pennsylvania, and therefore any discussion of issues related to other states must considered within that context. In addition, my comments are not intended to create a legal representation but merely to respond to the limited facts presented by the question. Any opinion herein is not meant as a precise statement of legal rights or as a recommendation of any particular course of action. A more complete legal review can be obtained through local counsel.
I feel that he should neither have discussed your case with your mother, nor quit as your doctor. You appear to have grounds to complain to the Medical Board of California, but your damages do not appear large enough to justify anything more than small claims court, if that, depending on certain rules relating to notice for medical malpractice--hardly worth it.