Could it be an ulcer?? I thought an abscess was the sign of an infection. I had horrendous toothache last year and after a few days of suffering I noticed a swelling on my cheek. Dentist said it was the abscess and I needed Antibiotics before he would touch the tooth Ulcers are pretty sore too. Maybe have a few rinses with salt water and see if that helps
If it's not sore it could be a number of things, could be a cyst? Have the teeth had much treatment on them in the past? Sometimes where there is chronic infection, you can get a collection of pus around a dead tooth which can cause swelling but no pain and can be drained out through the tooth in most circumstances.
Ulcers are generally quite sore.
Abscesses can be treated under local anaesthetic, even more so the painless ones. Let us know how you get on!!