Pain, swelling, & redness are simple signs of infection. They can go away quickly with megadosing vitamin C (or other natural immune boosting methods), a return to an unprocessed/low-grain&sugar diet, and/or antibiotics. (The first two being means to aid the body in fighting the particular infection, the last being a means of obliterating nearly all bacteria in the body.)
An abscess is a sign of an infection that the body has decided needs to be contained, b/c it isn't succeeding in kicking it out. It is just a wall the body builds around the infection to contain it, and a hole in the gum is a sign that it is draining properly.
If the pain doesn't fade on its own, or abscess properly (a good abscess should no longer hurt), it should be watched carefully. Rapidly increasing pain, or (rapidly or not) spreading redness/swelling (such as to the cheeks), are signs of spreading infection. According to the author of Cure Tooth Decay (who is on this board sometimes!), his daughter had swollen cheeks and still they were able to stop the infection. At what point you quit using natural means to fight it and go for the antibiotic shot is up to your comfort level. My son had two abscesses that stayed painless for 2.5 years till they fell out, the one exception being on Thanksgiving once he had pain, but the pain was gone by time we found anyone open. His adult teeth came in strong & healthy, and the gums which once looked all bent from the yucky teeth now are beautiful.
Most dentists assume parents will take no responsibility for infection and so they say that as soon as infection appears, it must be rooted out. And even a cautious dentist who lets you wait-and-see will typically say that at the *first* sign of pain (in a tooth already abscessed), you should run to the pediatrician for an antibiotic shot, b/c the worst-case-scenario is an infection left unchecked until it reaches the brain. I think I'm closer to that in my personal comfort level than I am to treating even a swollen face naturally, but there are many places to be, and the key is being an informed parent who is watching, as well as listening to your gut feelings.
So the progression seems to be cavity -> pain/swelling/redness -> abscess -> pain -> spreading pain/swelling/redness, and the progression can usually be stopped or slowed at any point by returning to nourishing foods (that especially includes mama if she's breastfeeding, esp. if bf'ing a lot) & other means of boosting the immune system naturally, or it can be stopped by antibiotics/extraction/rootcanal.
I'd definitely check with your dentist to get his/her ideas and also read up to verify what I've said, lol. I'm not a dentist and I don't play one on TV and I didn't stay at a Holiday Inn last night.