Holly,
Welcome to OCF, glad you found us my dear, sorry you had to!
Trismus is common in oral cancer and there are exercises and the like to help, therabite would also be a tool for. The pain you are experiencing isn't normally associated with trismus so most here will not be able to relate.
Your Dr's are saying that your pain is neuropathic (nerve pain) and the reason it's so intense is because it involves the Trigeminal Nerve. Trigeminal Neuralgia (or TN) is one of the most painful conditions known, so it makes sense if you have trigeminal nerve pain you are on so many drugs. Generally the first line of treatment for TN is Carbamazepine and I'm surprised it's not on that list. Second line treatments usually go to a mix of opiate(oxy)and an anticonvulsant (gabepentin/neurontin & trileptal) however low dose antidepressants are used as well.
Facial nerve pain I also suffer from, thankfully not from the Trigeminal Nerve (Cranial Nerve 5), but it's very painful due to how closely tied all of the nerves in your face are (most terminate at the trigeminal nucleus). My 7th cranial nerve on my right side was severed during my mandiblectomy, paralyzing the right side of my face, I had a procedure called a CN7-CN12 switch nerve graft that pulled my 12th cranial nerve (paralyzing half my tongue) and grafted it into my damaged 7th cranial to try and restore function. Sadly it didn't however it did help ease the neuropathy I experience a little.
Neuropathy is tricky and can be hard to treat. For me until I got a handle on it, I used marijuanna and it did shut down the pain at night and allowed me sleep. Lidocaine can also be used and is effective in some cases as is Transcutaneous electrical nerve stimulation.
Here is a link to the Mayo Clinic's write up on TN that may give you some options on treatment. Good luck, sorry you are in pain but hopefully with help you can find solutions.
http://www.mayoclinic.com/health/trigeminal-neuralgia/DS00446Eric
