I had a past dog in a similar situation as yours. His face would get so swollen because he had an infected tooth that needed to be pulled, but he was older and had heart issues. His murmur was really bad at that point.
The two options were to either put the dog under and risk him never waking up to pull the tooth or to just give him pain meds and antibiotics. He recommended to just give him the meds and that's what we did.
The swelling and pain went away pretty fast once we started giving him the meds. The swelling would come back every 6 months or so, but went as quick as it came. Never really was much of an issue. He died peacefully about a year or two after that of heart failure without ever removing the tooth. We definitely made the right choice not to put him under at that age.