I'm trying to avoid antibiotics for a tooth infection—any alternatives?

So, here’s the situation... I had a filling fall out of a tooth that had already undergone root canal treatment. Since the tooth was left open, an infection set in, and I was dealing with some pretty intense pain for a few days until I finally went to the ER. They patched it up to close it off and prescribed me some Augmentin. The doctor there suggested that I probably bit down on something too hard, causing the area to become inflamed and irritated. The following day, I saw my regular dentist, who told me we need to continue the actual dental treatment and that I absolutely must finish the course of antibiotics to prevent the pain from returning.

Now, here is where things get confusing: the pain actually subsided on its own after the ER visit, even before I started taking any antibiotics. It makes zero sense to me why I need them if the issue was just simple irritation from biting something hard. To make matters worse, I have had a truly miserable experience with antibiotics in the past; the side effects I dealt with were significantly more agonizing than whatever ailment I was originally trying to cure.

I am hoping someone here can offer some clarity or guidance...