About this time last year I had an abscess in one of my lower left molars. Unfortunately the tooth was too damaged for a root canal and had to just be pulled. As soon as I left the dentist office I filled the antibiotic script
This was the Wednesday before Marine Corps 50k and I still did the race. Did I do as well as I wanted to? Hell no. But that was more due to the way antibiotics affect my GI tract and I had to hit the porta-potties every couple of miles after the 15 mile marker.
There's no adverse effect running with an abscess as long as you're treating the infection. So treat the infection and do what you can running-wise.