As Karen has said, Depression should not be anything to be ashamed of. There is a terrible stigma of mental illness in some people but mental illness should be treated the same as physical illness. (Darren gets off his high horse now! lol)
Who you tell is your decision and some of that will be guided by how you think people will react. I think you will feel a great sense of relief in sharing the problem with someone. Talking to your councillor is a great idea. They may have suggestions on the best way to tell people as well.