How do I tell the doctor?

I'm 16 and I've felt what I believe to be depression for years now. It's taken me a lot of time to work up the motivation to seek help, but I'm still too scared. Unfortunately my parents don't understand mental illness and think my life is too easy for me to have any kind of "issue." They also tend to delay doctor's appointments of any kind for as long as possible, so I figured I'll be better off if I tell my doctor at my next regular appointment.

The issue is that I'm too irrationally embarrassed and guilty about what I've been feeling to even tell close friends. I don't know if I can work up the courage to tell a complete stranger. Is there any way I can make this easier? And what do I say, exactly? Do I just come out and say "I think I'm depressed"?