I couldn't eat anything unless I was by myself, or with my family for 3 years. It was the most horrible thing, especially when I thought I could try it out again after a few months, and would feel like I couldn't swallow, like I was choking, and nauseous (even though I hadn't eaten anything). And making excuses (mid anxiety attack) is never any fun at all. Several times in restaurants, I would try a few bites, and things would be going well. Halfway through the meal, I would realize that I'm full, and then the anxiety would hit. I was afraid that I would now feel nauseous and have another panic attack. And I did have to run out of several restaurants, which is just a nightmare. Sitting in a dark restaurant evaluating escape routes while attempting to seem calm and normal is something I'd rather not relive

I am very lucky that after a few years it passed, probably because I increased my dosage of Sertraline (Zoloft) from 100mg to 200, a very large dose.
A year later, I am back down to 100mg and have less problems with eating in public. I never figured out what caused it really, but my guess is that my anxiety manifested itself in the fear of feeling nauseous. This, in turn, made me fear eating in public because of the possibility of nausea, and the potential awkwardness that would ensue if I had an anxiety attack in front of other people and hurled all over my dinner companions. So in the end, it was essentially anxiety of getting an anxiety attack in public, that was probably randomly manifesting itself in food. It's a hard one to work around.

I think our experiences are somewhat similar, and what worked for me was increasing my dosage, waiting a few weeks, and slowly trying to eat out again. Or try eating in a public park, then an informal restaurant. I still sit close to the door if I'm feeling anxious at all just in case I can make a fast escape. It's the possibility in my mind that I could escape if I wanted to, that makes the whole situations better.
Anyway, I hope that helped. I hope you figure it out, because it's horrible, and I can relate.
Good luck.