I assume that you are asking because you do not want to seek help from a dentist and take Antibiotics ? An abcess can be very dangerous, it is a poisionous infection. It can lead to serious infection throughout your body. I did not know this when I had one, and it was just an annoying bump on my gum.
I was taking large amounts of garlic internally for a parasite infection. A couple of months later, I realized it cleared my abcess at some point along the line. Garlic is an amazing natural antibiotic. It will take longer than the pharma route, but it will not cause the other longterm effects that Antibiotics do, and has many other healthy benefits as well.
It may burn, but you can also apply it topically, maybe make a poultice with mashed garlic and some BF&C (you can purchase from Uniquity or make your own), or even just mashed garlic applied for a few minutes several times daily. Oregano oil is another good suggestion, but I can only attest to the fact that garlic is what cleared mine.