Stop thinking so highly of yourself. There is nothing humiliating about them. If you get feeling of humiliation from someone watching you work, then you are going to have a bad time working in a team.
But, for others like an introvert, the whole process is like dancing in a circus in front of the people (with each one of them asking you do something at the sametime).
But maybe my saving grace here is that I don't fear pressure in that kind of situation...
This is 100% in your head and about your attitude. Your ego is the problem, nothing else. I'm introverted as fuck, but I realize that this is part of interview process and if you act like a self centered cunt, who isn't willing to do a simple task like writing little code on a board, you aren't worth the effort for most projects.