Maybe for a while. You should still have it looked at. The SIL of a co-worker died from a tooth infection a couple years ago, and my stepbrother had an untreated abcess that erupted on his face and left a HUGE nasty scar.
I am struggling with dental problems right now as well. I feel your pain.
Most likely it wasn't an absess at the tooth root. Maybe it was just food debris under the gum? Even sinus problems can make a tooth hurt.
But regardless, you feel better now and that's important. If it kicks back in, I'd suggest you head to the dentist. Most of the time, even after antibiotic, the abcess comes back later with a vengence.