There are women who don't shave either, and doctors aren't there to judge your adherence to cultural standards of beauty; if you wouldn't shave if you weren't going to the doctor, don't shave just because you are going to the doctor. If it makes you feel better, I've never come out to a doctor and haven't shaved anything in years, for a long time before I even thought I might be transgender, and no doctor has ever even mentioned it (and it's very obvious). If you want your doctor's help in getting to an endo or therapist, you'll need to tell her, but otherwise there's no reason to come out unless you feel like it.
Also, you can always refuse a test, like a breast exam, if you're uncomfortable with it, regardless of whether you're trans. If you're still living at home with your mom, chances are you don't medically need a breast exam anyway, or you can self-administer if you're concerned and only bring it to a doctor's attention if you find something unusual.
As for everything else, it's actually pretty common to have anxiety about phones. I also have a lot of trouble talking to people if I can't see their faces. When you're calling to make an appointment, it might help to write out a script and just read off of it, as you're likely to be leaving a message anyway. Hope this helps!
