I used to not be able to eat in front of others, but I don't have that fear anymore. For most of my life (until my late teens), I was overweight. Lunch time was an absolute nightmare for me because I felt like people were looking at me and thinking, "why is she eating that? She's fat!" Many times the other kids would say rude things or oink or what have you when they walked past me. I couldn't walk across the lunch room or even stand in line without feeling extremely uncomfortable with anxious thoughts and symptoms. Also, whenever I'd find a secluded place to sit, a large group of people would inevitably come and sit next to me and I felt so uncomfortable and intrusive with people talking and hanging out and there I was, the stranger sitting there looking out of place and like an idiot. It got to the point where in middle school, I'd avoid the lunch room all together. I'd buy a pop and a cookie from the vending machines and then retreat to the bathroom, where I'd stand in a stall and eat and drink and write in my notebook until the bell rang for the next class. It's extremely embarrassing to admit that, but really I had no other option; the anxiety was so strong and pervasive that the only place I felt safe was in a bathroom.
I also had a traumatic experience once (I was 17 at the time) when dining in a hospital's cafeteria. My dad was recovering from a heart attack and my mom and my sister and I went to go eat. I jokingly said to my mother, "you shouldn't put butter on your brocoli, mom--it's not good for you." A nurse who was sitting within hearing distance one or two tables away got up and when she walked past us she said something to the effect of "your the one who should be watching what she eats" and looked at me with a disgusted look on her face. I got so upset that I started crying and I felt so angry and frustrated that I wanted to throw the chairs and topple over the tables but I didn't do that. I was having a really, really bad day as it was, but then someone had to come along and say something hurtful and mean when I was at one of my lowest points.
Now, I don't feel so self-conscious about my body, so eating in public is not a problem for me. I'm not sure if I'd be able to eat in public if I was still overweight, though. I'd be afraid that someone might say something mean to me.