I experienced something a little similar.
Did you have a root canal after the pain started?
Root canals are somewhat controversial.
I ended up pulling my tooth and it did NOT help me. I had no pain originally, but was to have a crown put on, many weird things happened and ended up with bad pain. No one actually saw an infection, yet I was given massive dosages of antibiotics and a root canal and then my tooth was pulled. The pain worsened and worsened. I spent thousands and thousands of dollars.
In my case, it was neurological damage very likely caused by the first dentist attempting to put on the crown.
I am surprised a dentist actual used the word "neuralgia" in your presence. Are you in the US?
A Tricyclic medication like Elavil might help.
You might need to get a few opinions before narrowing in on what the the problem or problems are. And neuralgia should be considered.
Unfortunately, you likely need an MRI, but it doesn't always show neurological damage. I have atypical neuralgia and it didn't show up on my MRI. But my pain in the dentist chair was severe , sharp and almost electrical. Afterwards, it is more severe and boring...like a severe pressure...very hard to describe. It is in my jaw, face and ear primarily. Consider seeing other dentists for opinions and a neurologist.
What a very difficult experience. I hope you get some answers soon!