Hi! Please ignore the idiots on here. Bulimia is a disorder, think of it like having an injury - but to the brain. You would never hope for a broken leg to just go away without treatment, this is the same situation. Go get professional help NOW. They will help you work through it and it's going to be a long road to recovery (months if not years), but you can do it. The longer you wait, the deeper the habits become and the harder to fix. As for training / racing, internet advice can't say much. Some athletes are told to stop training completely because their bodies are already very weak. Others are told to keep training (at lower intensity) while they go through therapy because it might not help to lose all your routine and daily rhythm. And of course, your risk of injury is higher when you don't fuel your body. But whatever it is - please go see a professional and if your coach is an idiot and does not take this seriously (many are from my experience), don't listen.
For those making irresponsible statements on here about "just suck it up" - get lost! Or spend 3 hours researching it. Or live with someone who has bulimia for a month. So angry.