I used to be terrified to eat in front of people- same thing, I felt like they were staring at me and was so afraid I'd embarrass myself. To be honest, I got over by forcing myself to. It took a long time. First I made myself eat in front of people I was close to, even if just a few bites. I'd save the rest for later and just chitchat until the meal was over, eating privately later. And I would try to only eat around others when they would be focused on something else like the TV in a dark room. After a long time struggling to do that, I pushed myself further and eventually further. Now I eat anywhere, anytime. I still feel discomfort when I'm eating with just one person, us facing one another and in close proximity, but I shut it off. It's hard. I'm with you.