Is it normal if i can't work in public?

I think it's because I have social anxiety. This is also when I was in school. I just can't do work when I'm around people. Put me in an office by myself. I'll exceed. I guess this also is because I grew up reserved and I'm a private person and I'm just used to doing things by myself on my own time. It's not just learning how the work environment is, it's more than that. I have social issues and I literally get anxiety to speak loud because Im afraid of others hearing me or doing a task in front of people that I'm not familiar with because I'm afraid of messing up and looking like a fool and fuck up which is exactly what happened today at my new internship. It's funny at the same time because I know myself and knew this would happen sooner or later and the day was today and who knows how many more times it will happen especially that it was only the third day. Now I feel like either quitting and come back when I'm less social anxious OR explain this to my supervisor which she probably doesn't have time to take care of a mentally challenged child and some people don't take these things seriously. Like yes people abnormal people exist and I'm one of them. I have no idea what I'm going to do but I have to do something to prevent this from happening again because it's going to cost my career. I can't let my social anxiety get in the way of pursuing my career when I know I got it. I know I can succeed at these tasks but its like I HAVE be alone. When people are around me, I get choked up and distracted and then look like I have no idea what I'm doing and at the end of the day just look awkward. It's a bigger deal than what it sounds. Only those who have it get it. When I'm by myself, I'm fine and I can handle a task. I guess cause there's no pressure either? Idk but I'm stuck at what to do about this even more now because in school, I had the same problem. Always scared of speaking up even though I knew what I was talking about and when I would try joining clubs, when it came to working there, I'd get that anxiety again and I would just quit and leave the club. Like I said, it's more than a confidence issue. I have confidence and the passion. I can go out, hang out with maybe like 1-2 close friends only, know what I want to do in life, know how to get there, etc but this disorder of mine just takes over and I'm a different persona and it'll cost me. Oh and I have trichotillomania, touching my hair all the time, so that distracts me too. I have a lot of issues that ultimately can lead to serious depression.