jjlsongbird is absolutely spot-on! Trigeminal Neuralgia does not typically present with constant pain, but the atypical variety very often does. Also agreed - the positive results from the medication (probably carbamazepine or amitriptyline) are enough to establish at least a working diagnosis of neuralgia of some sort.

Your doctor should continue looking for a cause in order to determine a long-term therapeutic plan, but in the meanwhile is duty-bound to treat your symptoms.