An infected tooth hurts worse than anything else I've ever experienced. I want through hell with my teeth so few years ago. I had a lot of crowns, and as my gums receded a little bit from age, I started to get decay under the crowns. One tooth after another.
Each time, the only way to save the tooth was to get a root canal and then another crown. I had one done before I realized it was going to be a recurring problem. Another tooth had so much damage to the roots than I had no choice but to have it removed. IF I was made of money, I could have gotten an implant (HA HA). I had dental insurance at the time, but it only paid 50% for crowns and root canals, implants weren't covered at all, AND there was an annual maximum that was several thousand dollars LESS than the cost of fixing one tooth.
It quickly became apparent that there was no way I was going to be able to afford to fix them as fast as they were falling apart. I researched dentures, and although most of my front teeth were still in decent shape, i soon found out that partial dentures cost a lot more than full dentures. Long story short, I ended up having them all removed and getting dentures. I was only able to wear the lowers for a few years before I gave up on them. Still wear the uppers for looks only, and take them out to eat. It's not great, but I'm not in pain, and I can live with it.
My advice to you is to try really hard to find some way to get that tooth taken out, because that infection is not going to go away on its own. Getting a simple extraction is actually relatively cheap, compared to the kinds of procedures that are needed to avoid losing a tooth. Getting that tooth out of there is absolutely critical; anything beyond that is extra, afaic.
I don't know what resources are available where you live, but around here, there are some cut rate dental clinics that are better than nothing. (Your county health dept. may or may not have something to offer.) My daughter needed dental work when she was too old to stay on our insurance but still didn't have a job with any health or dental benefits, and she found a clinic that did the work for much less than a private dentist would have charged.
Put up a gofundme if you have to. Call around to find out what the going rate for an extraction is in your area, so you know how much you need, put up a gofundme, and then post the link here. I'm sure there are lots of people who will be willing to kick in a few bucks, including me.
It's absolutely ludicrous that people have to suffer like this or scrounge around for resources in the richest country on earth, but here we are.