Should an antibiotic taken 4 days for a sore tooth be taking the pain away already?

I finally got a script for Cephalexin 500mgs taken 3 times
a day until gone——36 capsules. I have taken them for 4 days.
Should I be feeling less pain? I really cannot tell which
tooth it is only that it is the lower back teeth in my mouth.
It is actually the gum on the inside of my lower back teeth
that has the pain. Dentist is on vacation and no I cannot
afford a root canal or even an extraction for that matter.