That's horrible that you experienced that
By doctor do you mean just a General Practitioner?
The way I see it there are (at least) two potential ways you could tackle the visit to the doctor:
1. Go with your mum and tell the doctor about the anxiety problems but not the abuse. Ask for a referral to a therapist.
2. Go to the doctor but ask to see them one on one without your mum and explain that you suspect your anxiety difficulties are related to childhood abuse, your concerns about confidentiality, and that you would like to see a therapist.
(assuming that you aren't comfortable telling our mum just yet)
Basically, either way: try and get a referral to a therapist. You can then tell the therapist about the abuse in private sessions, one on one, and they should be able to help.
(you can choose which gender of therapist you would like to see, btw)
*If you are still under 18, the doctor and possibly the therapist may have a legal duty to report abuse to authorities, but I'm not at all sure of that.
It's something you might have to google to find out what duty of reporting laws exist where you live. It's quite possible that you may be able to ask them about confidentiality before deciding to reveal anything.
Basically, you only have to tell people as much as you feel comfortable with at a time, and you are well with in your rights to take the time you feel you need. I'd encourage you to make seeing a therapist soon a goal though.
Good luck! I'm so sorry you suffered such abuse
It's no wonder you have anxiety difficulties. I hope you know that what happened to you was not in any way your fault. You're not a "freak". There are others like you out there and there is help available. I hope you will be successful in getting that help.