I wish I could have alone time with my doctor but I don't know how to tell her.. any help?

Tell the nurse that you would like not to have your parents in the room. You just have to ask.
Or you tell your parents that you don't want them in the room.

Are you just wanting to be grown up, or do you have private questions to ask?

Private questions an how would I phrase the questions?

private questions an how would i phrase the questions?
The best thing to do is to make a list of them on a piece of paper, then tell the doctor you want to ask some questions, and then just ask.

Can you list them here, and I (we) will help make them sound good?

Like about menstration, puberty, and vaccines

I don't mean to be rude but things like menstration and puberty should be easily talked also to your mom, those are normally "mother/daughter" talks, or a aunt or older female family members helps you with. This is just part of growing up and nothing to be ashamed or confused about. I had five boys and had all the talks of puberty, sex, growth of hair and other male issues.

As for vaccines, not sure why that is even private,

Not that you can not ask for privacy, but I assume you had sex questions or something, not normal questions that are often done at home.

I was very uncomfortable talking to my mother about periods and other personal matters, I think it is perfectlya cceptable for you to want to talk to your doctor alone, at any age. What would your mom say if you asked to go in alone?

If you feel like you don't want to tell your mom, you can always call the doctor's office a head of time and let the receptionist know that you would like to have some private time with your doctor. It's normal to be embaressed when it comes to the changs in your body. If you don't feel comfortable asking your mom questions, the doctor is the next best person!
Good luck.