It may help for the short term but the infection is inside the jaw cavity. You really do need to call 3-5 dentists in the morning, desribe it to them, tell them you have a couple more teeth that need extracting, find one that will do the cut and lift method (oral surgery removal method, they cut the tooth in half and then lifet it out in halves) and he can cut into that area at the same time and fully scrape it clean. I'd get it done asap.

Then be sure to tell everyone you know about your experience with other dentist. Word travels quickly about doctors/dentists.

'I got the worst infection after having work done by that dentist..'

It's his reward for caring so much about you.