I'm in school and I've run out of classes, I've had the whole class staring at me, I've run out of a hall of 200 students etc etc and to be honest - they don't care half as much as you do. When I had my first panic attack in school I got so nervous when I had to go back to that class but no one even noticed or thought twice about it, you know? I know that at this moment you're probably feeling like that's not true, but I've been there!!
I would say go to that class and face your fear because the longer you leave it, the more afraid you become and the longer it festers in your mind. And if it was me and someone did ask, I'd probably just say "oh I wasn't feeling too well" and that would be the end of it!
Remember, there is no reason whatsoever to be ashamed of anxiety!