Hello from JustAnswer.
Your description does sound consistent with trigeminal neuralgia and I assume that none of these doctors have detected any abnormalities on neurologic exam, which is one of the key criteria for diagnosis of trigeminal neuralgia. There actually is no test that can prove that trigeminal neuralgia is present. However, imaging tests, such as an MRI, can be done to exclude other conditions that can cause external pressure on the trigeminal nerve.
You have already been tried on several medicines that are recommended for trigeminal neuralgia. The medicine that has been studied the most over the years is the Tegretol, but the gabapentin/Neurontin and pregabalin/Lyrica have been increasingly use since their introduction. Another commonly used medicine is lamotrigine/Lamictal and a less commonly used medicine is phenytoin/Dilantin.
If the various medicines are not able to ease the pain, then the next consideration would be a procedure for relief of trigeminal neuralgia. A surgical procedure, called microvascular decompression, has the best evidence for long-term success, but would require a Neurosurgeon that is skilled in the procedure, and if you have limited access, this specialty may not be available.
So, at this point, if the current medicines are not sufficient, either because they are ineffective or are causing intolerable side effects, then the usual next step would be to try a different medicine, such as lamotrigine or phenytoin. An MRI would be able to exclude other conditions. If the pain is persistent, then it would be appropriate to seek referral to a Neurosurgeon.