There are some great videos on YouTube regarding reversing dental decay with nutrition: high-quality animal fats, proteins CLO, etc. It's expensive and time-consuming and requires diligence, but I was pretty convinces when I watched them a few years ago. (The guy has his own protocol, and did not seem too interested then in this forum: you can enter "reverse dental decay" at YouTube and look at the videos.
OP is helpful for mouth/gum health but deeper infections such as yours need to be treated, as others have said, from the inside out. I'd try adding ooo (oil of oregano) to whatever base oil you're using for OP. (Caution: don't do too much at the outset: powerful stuff and when I first started oil pulling I went overboard with the ooo and got a canker sore on the bottom of my tongue that was so painful I was about to check myself in!)
When I had an abscess that was so painful that even Vicodin would not help, I packed it with cayenne pepper. Cayenne has a) circulation-boosting properties and b) capsaicin -- what makes hot peppers hot -- which contains an opiod-like substance that numbs. (A few years ago Harvard was trying to isolate this substance for eye surgery, etc.) Anyway, it hurts at the outset but is worth it if you are up late with dental/mouth pain, which is the worst!
If you're looking at a deep infection that has caused bone damage -- well, I'd be OK with getting the tooth extracted (rather than, as you mention, getting a root canal). What you want to avoid in any head-infection problem is the spread of bacteria to sinuses, ears, etc. It's been one time I've been willing to take Antibiotics -- though they will just temporarily treat the abscess you can see.