From what I've read, a true Trigeminal Neuralgia is not a common condition. TMJD can cause nerve pain.
The Trigeminal Nerves can be compressed by muscles, muscle spasms, damaged surgically, or irritated by other diseases.
Mine were surgically damaged and I was offered Tegretol. I had to have blood work and a liver work-up, BEFORE I could take it and was told these tests would be repeated often to insure that the drug was not causing serious problems. It's really rough on your liver. I decided not to take it.
It sounds like this diagnosis was made rather hastily and the proper tests were not done beforehand. It is a very strong drug and can have severe side effects.
I personally would try something else and I'm not sure what to tell you to do. I believe this is not a drug that should be just handed out like Tylenol.
This kind of pain is not easy to deal with. Your idea of a visit to the ER might get her something to take until she can have the proper test.