Got visibly drunk at a company outing and threw up in front of everyone. Should I just quit now?

So, I'm not even sure what to do. It's my first time ever going to a company outing, my first time ever drinking, and my first time ever getting drunk enough to vomit multiple times.

I never made a scene or anything. I was coherent and could stand up straight on my own. I just ended up getting incredibly ill.

I'm just so humiliated. My coworkers and superiors all saw me throw up (into a vomit bag, thank God) on the bus ride home and I'm 99% sure that I'm going to be pulled into HR. I don't even know if I should go in since this has probably gotten back to the owner of the store. I mean, this is a part time job, so nothing serious. I just don't want to do the walk/talk of shame.

What should I do? Just quit and pretend I never met these people? I have no full attachment to this workplace but I do want to move to another town and hide forever until the end of my days.