It does sound like the exercise is what's causing you to gain weight. Here's what you have to ask yourself: is it more important for you to be strong or thin? As a dancer, I would assume that strength and stamina are more important to your future career, so as painful as it is, you might just have to live with the weight if you want to be the best dancer that you can be.
Binge eating is hard to deal with, but it helps to keep your house stocked only with healthy-ish things...that way, when you do binge, you have no chice but to binge on things like vegetables and hummus.
I'm not in your situation, but I have a friend who is a trapeze artist, and she gained some unwanted weight. After looking around, she found a personal trainer who understood the needs of her profession and made an exercise regimen that was right for her and suited her needs. You might want to consult with a personal trainer who focuses on things like ballet or gymnastics, and can better understand your situation.