Could it count as a eating disorder when you eat a lot and then make yourself throw up?

Yes - Bulimia Nervos: What you describe is one of the more common eating disorders and it can range in severity. Therapists with experience in treating it are often quite successful if their patient wants to resolve the problem or is willing to try. It is much easier to handle if you get an early start, so don't put it off. Real physical damage can be done. You'll be glad to get it behind you.