Some doctors are a bit lax when it comes to parents and children's privacy, but by law, she shouldn't be able to tell your mom anything unless you do something like threaten to hurt yourself. When you talk to the doctor, you should state (just to make sure) that you don't want her to tell your mom about what you are saying to her. She should respect that privacy.
However, I will say that you should probably tell your mom what is going on with you. Teenagers keep things from their parents because they are afraid to get in trouble, but a lot of times telling them prevents a lot of trouble. Maybe your mom would get upset (depending on what it is), but she may not stay upset. I had a friend who got pregnant when she was a teenager. She did tell her mom and her mom did flip out, but eventually, she accepted it and they got through it together. It would have been so much worse if my friend had gone through everything without her mom there.
Yes, there are situations where parents are abusive or something like that, but most of the time, that's not the case. Really think about your mom and your relationship with her. You can probably trust her a lot more than you are. If she thinks you are being secretive, she probably is making it worse in her mind than it actually is. If you trust her with important things, then she will trust you to make right decisions and that if there is something that you will come to her. She loves you and wants what is best for you.
Also, if it's just the yeast infections you have posted about before, that's nothing to worry about. Girls get yeast infections, whether they are sexually active or not. If that's all this is, just tell your mom.
I wish you all the best. Good luck.