I have TN but have not been diagnosed with it as it is all part of RSD/CRPS.
I recently had a crown put in and they did not do the proper blocks, so my mouth is in the flare.
What is settling it down for me is Klonopin. Also using warm salt water several times a day. Let it swish gently in the mouth and let it sit in there as long as you can do it. Also try warm sugar water. ( the why I cannot explain) A doc came up with it sucessfully as it is simular to a Mannitol drip used to be used sucessfully)

If you could get an anesthologist in a pain clinic to actually teach you to do your own sphnoid block would be very helful. Mine taught me in NM.