Dentist appt next week/ severe tooth pain/ on penicillin and tylenol (acetaminophen) 3 for 2 days/ now swelling worse and pain unbearable. Should he go back to ER?

Yes. If the pain is getting unbearable and swelling is increasing then you need to be attended to ASAP. Would be better if the tooth were attended to by a dentist so that the source of the infection can be treated and the problem mitigated. Please take action.
Another DDS. If your dentist won't see you sooner, find another dentist. ER won't solve problem.