First things first, you need x-rays done to rule out tooth involvement. You aren't going to be able to tell anything by just looking in the mouth. If there is tooth involvement, they will need to extract the tooth, lance, then drain and flush the abscess and have them culture what they drain. Without tooth involvement, they'll still need to lance,drain and flush, send off for a culture, then go home with antibiotics and pain meds. Both Meds are VERY important. See if you can get Clavamox, TMS, anything but Baytril.
You need to have this taken care of sooner rather than later. Abscesses can be dangerous because of the risk of infection spreading.