Hey Dez,
I just went through this process last week actually at my school.
You can and should ask her any questions you feel it necessary/important for you to ask. She will know the answers. I was prescribed an SSRI and it does not affect my birth control. However, that does not mean your medication will be the same or is for the same purpose (my medication is for major depressive disorder and general anxiety disorder (I am taking it for MDD)).
The appointment should not be too diffcult: she will probably ask you questions about what you are experiencing, explain to you the type of medication she thinks will be best, tell you which medications she prefers prescribing and the side-effects etc. I know that my medicine does not have many side-effects and what I really like is that if it does bother me, I have the option to split my pills in half if I find the side-effects are too much. I've been taking them without splitting them and I'm feeling okay other than the expected side-effects (and how I feel from those are minor) and so I am going to keep taking the dose I was given and see the doctor this week.
Also, she will want to see you more often at first once you are taking a medication because she will be able to ask you about how it is affecting you etc.
Another thing I just remembered is that it may be helpful for you to ask your school's health center if they have medications from a local pharmacy delivered to the school for students. I know that the pharmacy drops off medication for students to pick up everyday at 4:00 which is nice for people like me who cannot drive or who do not have time to get to the nearby pharmacy.
Lastly, in regards to your parents knowing, they are entitled to their own views about mental health however you are at an age where you choose what treatment is best for you. If that means taking medication, you have the right to receive medication and they should not be able to hinder you receiving it.
If you are at home and need to pick it up from a local pharmacy is there one you can walk to? You can tell them you are going on a walk and go pick it up on your own. You can also tell them you are going to be taking medication for depression, anxiety (what it is specifically you are getting it for) and that you are taking it because you believe it will help you and that it was recommended by the doctor.
Stay strong even with their negativity or bias towards this, your health is important and you deserve and should do what is best.
Take care.
I hope this helps and if you would like to talk more, you can
PM me. I know what you are going through. I just decided to take medication and I have not yet told my family as well.