Firstly, I'm really proud of you for being able to stop cutting and recognize that it's like an addiction! It really is, and, because I'm a dork, from what I can understand it IS an addiction, scientifically or the like.
Now about your family doctor... perhaps you can ask your parents if maybe you can see another doctor the insurance will cover? If you don't want to go into full detail, you can simply suggest you're not really comfortable seeing this doctor anymore. I hope things work out