Seems like for the ifection they would need to give her antibiotics to clear up the infection before they would do the surgery.

You can always go to a tractor supply and pick up a bottle of penicilan. It's liquid form but giving a dog shots isn't a big deal. That will at least help things along.
Might sound dumb but get some people tooth ache medicine and swap the tooth that hurts with it. Doing those two things would buy you some time to figure it out.