It sounds like a blood blister. But i would go to your dr if your not sure.
Yes, definitely go to your doctor asap. There's many things it could be, if it gets bigger it most likely is some sort of spider or insect bite. Don't squeeze it unless you think it might be an ingrown hair. But if for some reason you do and it's like a pimple but pus won't stop coming out, then that is a cyst, but I advise not to do that. I've had cysts before.
I'm not sure. It could be a bite from a spider or insect or it could be a cyst or it could be staph. Since you said it was red and hurt it sounds like its infected so I would go and get it checked out, you don't want any infection getting into your blood stream and it affect the baby.