I haven't had any dental work done for years, as I had all my teeth out years ago. So, no more of that pain and anguish. I'm glad of that now, especially since I now have this COPD. But I will say this to you: If you go to have a tooth out, they will use a local anesthetic rather than a general one, which is the kind you would need to be worried about. The local will get you through most of the immediate pain, and will be okay from there, as long as you make sure any infection is cleared up before you have the tooth out. That is imperative. You must make sure that if you do have an infection it is cleared up with antibiotics first. Then you should be good to go. They should have already told you this (the Dentist AND the Doctor). The two things about a dental infection are - that it can kill you, and that when you have one, no local anesthetic can deaden the infected nerve. The deadening simply does not work. At all. So, if there is an infection, they will need to give you antibiotics for a couple of weeks or more to clear it up before proceeding.
FYI - An interesting fact about dental infections is that, up until modern dentistry came about in the 20th century, up to half of all human deaths were caused by dental infections. Evidence of this is found in the histories and medical journals all the way from the dark ages and renaissance all the way to the early 1900's! Why? Because, while an even larger percentage of deaths were caused by infections of all kinds, such as with broken bones and internal organs as well as injuries, not everyone suffered those, but literally everyone did suffer from dental problems. And like Paul Harvey always used to say, that is the rest of the story!