I do not think you should disclose any mental health information to your supervisor.

First of all, you have already mentioned that it is interfering with your work. So, the minute you tell him you have "depression" or "bipolar" or anything, he/she is already going to see that it is affecting you.

Mental illnesses have an incredible stigma associated with them.

My opinion is that you should talk with your boss and ask if it would be acceptable that you take your lunch hour late (or whenever your appointment is) because you have a personal matter which requires attention. Also, reassure your boss that if your lunch hour appointment runs later, you will make up the time during the day.

Mentioning any type of mental illness is a danger. And while under the American Disabilities Act, you are protected from being fired, it is very easy to "come up with other reasons to fire someone" ~ such as your work performance has decreased, the organization is cutting back (particulary a small organization).

Danger, Danger, Danger.