Devonguineas, I think what you need to ask your vet is what could cause a swelling, which due to a potential tooth problem, that couldn't be sorted by antibiotics.
Before you subject him to anaesthetic and the expense, just ask the vet what the possibilities could be.
Abscesses sometimes need to be lanced before antibiotics can help ... I hope I am right in saying that though!
Have you any photos of the swelling that you could post? Apologies if you have already, but I am just doing a quick catch-up on the forum.
Rikkyboy, one of my piggies, has a swelling under his chin but I know that isn't an abscess or tooth problem, it is a growth ... and getting bigger! :'( He doesn't hurt him when I feel it gently, but I know it is getting uncomfortable for him and that he isn't his usual self! I have been to the vet so I know what the prognosis of his condition is. :'(