I understand what you are saying, hopeful, however one could easily insert any of a number of labels...in place of nurse....Mom, teacher, truck driver, etc.
It matters not what is expected of you, but rather what you expect of yourself. Yes, it may be important to try and keep somewhat quiet about being depressed being in the medical profession, but I don't think ANY profession is any more/less exempt really.
Give yourself a break...realize you're not a rock, or a lamp, and that it is normal to have these feelings.
I think once you cut yourself some slack, it will follow that you won't feel the necessity to be so concerned with what others might/may think. Surely, though, you need to work with your doctor...and work through this, as best you can. Giving up might seem easy, but think of your loved ones. Peace in the struggle....Take care...let us know how you are doing! :)