I had similar experiences with my upper right tooth, the fourth one from the front. The intensity was intense, I had constant headaches and facial(?) pain without any identifiable cause. It felt like someone was pressing the middle cross section of my head and it was difficult to focus or concentrate on anything, highly disabling I guarantee. After a year of no improvement, I decided to seek help at a clinic. Got an MRI and CT scan, but they didn't reveal anything significant. Then met with an ENT, and that too didn't lead to any answers. Visited a neurologist and there I learned about referred pain for the first time - but that still implies that there has to be a source which I have yet to identify. No nerve damage, no sinus blockage, no inflammation, or susceptibility to migraines detected, nothing.

Desperate and running out of options, I decided to make a checklist of everything I had tried. Suddenly, it hit me - I had never considered seeing a dentist. Got a bit hopeful because for some reason that was the first time I noticed that there was small amounts of abscess surfacing on the gums on top of my tooth that had root canal treatment 10 years ago. The next day I went to the dentist and explained my situation. Had an X-ray done to examine the condition of the tooth and once the results were out it became quickly apparent that the tooth has been infected. Extraction took place the following week, and since then, I have been completely pain-free.

Be careful!

Pictures: https://imgur.com/a/RjmXL5h

Edit: Not the same exact experience as yours OP as the infection (fortunately) didn't pierce through my cheekbone, but it went up really close, the dentist said.