Although my level of education and position at the learning institution I work for are not comparable to yours, and the specifics of your situation are going to be a major component in your decision; the defining issues in dilemmas such as the one you are experiencing are universal.
Being the pragmatic individual that I am, I can see (and I believe that you too understand this to be true as well) that the answer to your problem ultimately hinges on one thing and one thing only. Will the revelation of your struggle improve or hinder your career?
My husband, who works as a graphic artist has been fighting depression for his entire life, and he had a particularly nasty bout with it earlier this year. When he asked for my advice on the matter, I told him that because he worked for a small business whose owner is extremely involved in his work, she had a right to know due to the fact that it was directly affecting the quality of product being put out. He took my advice and has gained empathy rather than a negative stigma from his employer and colleagues.
That being said, I was hired as a high school Spanish teacher a couple years back. I was struggling with depression as well as anxiety issues. Three weeks into my first semester, the headmaster of the school learned of my conditions, stated that he never would have hired me to begin with if he had known, and asked for my letter of resignation.
Deeply understanding the need for a sense of community when illnesses such as depression arise, I would still say that so long as your work performance has returned to normal levels, you should not confide in anyone associated with your work environment. However, you may want to look into forming bonds with someone in a similar position at a different institution in conjunction with the continuation of your therapy.
Remember, a professional's reputation is one of his most important assets.