I have that problem too! For some reason it gets even worse if it is at night. When I feel like it is getting to much for me, I focus on my breathing and try to disassociate myself from the noise and the people. Take a trip to the bathroom or excuse yourself for a bit if it gets to be too much. A comforting thing to think about it that you are far from alone with this problem and there probably is another person in the restaurant dealing with the same thing! Drinking a lot of water helps me too. Also, avoid caffeine!
In general, try to conquer the fact that the feelings are JUST anxiety. That's it. Just your body being confused with the situation. Own that you are okay. Tell yourself you know better. I know, easier said than done, but the more you think it the more it works.
I dont like eating in front of everyone because I feel like people are staring at me as well. However I have gotten better at it lately. It was something I just had to get over because it was bothersome to eat anywhere.
Maybe use some comparitive thinking. I worked over seas for many years and saw upfront and close sever hunger issues. India, Pakistan and Kenya were the worst. Many people have no idea where their meal is coming from and search the garbage for bits just to avoid dying of starvation. We have so much in this country that many times take for granted all that we have. I believe all this has led to choice problems. Yes, there are chemical imbalances that can cause anxiety, but i have to think that most of our problems stem from the lack of understanding of who we are, what our purpose in life is, our relationship to our creator, unfullfilled goals, utilizing our creative side, and giving back to the earth what we have taken.