Im no doctor but perhaps you should realize that it's time to stop and that to do so you have to tell the people who know you and go see a doctor.
It is your health you are debating about and it shouldn't require "mustering up the courage". Your health is one of you number one priorities and pride and fearing humiliation or the like shouldn't even enter into question.
Ask yourself what is more important: your health and well being or what people might think of you? Even if people around you give you anything BUT support perhaps they don't deserve being in your life. Besides, bullimia is not a rare thing it happens to many people and when they do get fixed up they end up stronger and better than before! Once you start your journey to overcoming this disease you will realize that there is a light at the end of the tunnel and you will come out a better, stronger person! Good luck!