I've heard of Ketamine as another non-opioid approach to pain, I don't know how effective it is quite for pain or dental issues.

Dental pain is awful. I'm so sorry. I had a hospital-and-hydrocodone-worthy case of oral thrush a few years back and beyond losing the ability to speak...well, at all, for a time, I found myself slamming the counters with my fist so the new pain in my bruised arms took away from the roaring, unending pain in my mouth.

I can't imagine having that kind of pain for more than a day or two before being in a dangerous mental state with respect to my own personal safety.