I can tell you for a fact Turpentine works for a tooth abscess. I had a huge blister on side of the gum where the abscess was and so much pain and soreness. I'd take the turpentine and hold it in the mouth directly where the infected tooth was for up until I couldn't stand it any longer snd spit it out. It needs to be undilute 100% pure pine gum spirits of turpentine (Diamond G Forests has the BEST in my opinion).
Also if you can start using chlorine dioxide solution as s mouth was and add w few drops of DMSO right before you're going to use it because DMSO deactivates the Chlorine Dioxide within hours of mixing the two. If you're only using the Turpentine I'd say continue to use it until the infection is gone but shouldn't take long.
You should see some improvement within a few days but I'd use it multiple times. But it's also crucial to ensure there's no food stuck between or in a crack of a tooth. A Waterpik on semi low or higher if it doesn't cause too much pain in your mouth really really helps.