I think I may have social anxiety disorder. I have no trouble eating by myself, and I'm usually comfortable eating in front of my family and very close friends. My main problem is that when I'm eating with others in a public setting, I continually worry about throwing up and the embarassment that would cause. Now I shy away from going out with my friends because I don't want to face that situation. Sounds like you are right on track with your diagnosis.
Phobias often take a long time to get established, and once they do, they can become very ingrained.
Recovery requires a very active approach. Fortunately, there are treatments available which are extremely effective for this disorder. One in particular is referred to as exposure and response prevention treatment. There are many good self help books on social phobias.