I used to be bulimic and it's really hard to stop. At my worst I would binge/purge 5 or 6 times a day. So exhausting. I recommend you get therapy and learn what emotions you are experiencing when you do this and learn how to cope instead of stuff/purge. Also, Narcotic's Anonymous (NA) is for all addictions, not just narcotics and there are many people there who cut, are bulimic, etc that learn coping skills and bond with others who are struggling with the same addictions. Bulimia is an addiction and you qualify to get help there. NA is FREE and meetings are all over town at different times of the day/evening. Bring a friend if you are nervous to go, but I strongly urge you to go. You will get a key tag (reward) for being 24 hours clean and then one for each month up to a year and then one once a yr for remaining clean. The program works. Best wishes to you.
Do whatever your doctor says to do.
Then talk to your parents and find another doctor. You shouldn't be asking strangers on a website for this ... especially at your age.