I live in constant fear of my family finding out about my bulimia.
That must be difficult. Why are you afraid of them knowing?
I hope no one finds out about it because it would shame me socially.
Keeping it a secret will do more harm than good. You should tell your family if you cannot seek help on your own. They can encourage you to seek help if you cannot do it yourself.
I refuse to tell my family about my bulimia, because they're so happy since I'm thinner now.
If you've lost a lot of weight because of it then I really think you should tell them because you could be seriously harming your health. Your family wants you to be healthy, and the best way to do that is to talk to a professional about your bulimia.