The symptoms may be secondary to trigeminal neuralgia. The trigeminal nerve supplies sensation to the face. After surgical procedures on the face or teeth this nerve can sometimes become irritated. This results is severe lacinating pain. This condition is typically treated with anti-epileptics such as carbamazepine, oxcarbazepine, or gabapentin (Neurontin). You should discuss this possibility with the neurologist.
Regarding testing, an EMG (muscle/nerve test) can be done on facial muscles, but it is very limited. I would see what the neurologist finds first and then proceed with testing. Good luck.
You may want to look into TMJ (Temporal Mandibular Joint Dysfunction). Sometimes when we remove something like a wisdom tooth, the other teeth shift and then the upper and lower jaw become misaligned. This misalignment stresses the mandibular joint which can cause an array of symtpoms such as pins and needles along the face, ringing in the ears, pain in the ears, pain on top of and behind the head, eye pain and temporal pain to name a few. It's an excruciating condition that needs attention. I would see someone who specializes in TM disorders.
Neurologists are well trained in what they do but this is something they will NOT be able to help you with. Gaurantee!
Crusher