Does your university have counseling services? If so, you might go in and speak to one of them. They can help communicate with the Dean and be sure everything is documented properly so accommodations can be made if needed. If you don't go through proper channels, professors aren't really obligated to make accommodations for you (and generally won't).

Worse case scenario, you can arrange to take a leave of absence from school while you get your depression better under control. I had to do that my last semester of college. It completely terrified me to have to do so, but it was entirely helpful to take a few months off and just rest. I was able to go back the next semester, finish up my coursework and graduate. It seemed like the end of the world at the time, but in retrospect, it was a small glitch in the scheme of things. I went through the counseling services department, which coordinated with the Dean and made sure everything was done properly so I didn't have to pay tuition when I returned, etc.