Were you bullied when you were you were younger, or is there anything else that has happened that you feel could have contributed to this shyness and lack of confidence?
Excellent questions. You should answer them honestly - not necessarily here, but to yourself.
Years ago, I was in a difficult relationship that completely dissolved what confidence I had. When I was finally free of that relationship, I suffered the same panic while in public. I was forced to overcome it (to some degree) because I have a daughter who needed/needs to see healthy interaction between people. I put on a front while with others, smiling and concentrating on what they were saying so that I didn't have to think about the overwhelming 'need to run' that you described.
I wish I'd sought help for it but, honestly, I didn't fully acknowledge it as a problem until recently. You're ahead of the game by recognizing that this is something you want to overcome. I'd suggest speaking with your doctor. You'll be amazed to learn how common it is - with or without past trauma to instigate it. Your doctor will be able to help, and if s/he can't, you'll be directed to someone who can.
Above all, be patient with yourself. This fear is possible to squelch, but it won't happen in a day.
"The others don't like my interviews. And frankly, I don't care much for theirs." ~ Freddie Mercury