Is there any chance it could be an atypical migraine instead?
Did the pain start after physical trauma of some kind?
I have both migraines and atypical trigeminal neuralgia. The ATN came on over a year ago right after some horrendous and peculiar dental work.
There was lots of confusion afterward....and finally I was sent to a neurologist who dx'd me as having ATN.
In terms of something natural, capaisin cream , which is from a pepper, always helped me a little (and still does). I would rub this cream on my face where the pain was at its worse and get some relief. One has to be careful though, as the cream can burn the skin and of course, you can NOT get it in your eye!!!!
I go to a website for tn pain (I put it in the top thread here/USEFUL SITES) that I would highly recommend. There I met a poster who has a PhD. His wife has ATN and he had done a lot of research on the best meds to treat ATN. Gabapentin does provide relief for many people. So do the Tricyclic medications like Elavil. Together, they often work well.
My regimen is slightly different, but works well. I have posted about it a lot here because I am very excited about it...as the pain I was having before was HORRIBLE.
After trying many different medications, I now take:
Desipramine: Pill nightly
Compounded Cream: Containing Gabapentin, Lidocaine and Capsaicin
I also did acupuncture for many, many weeks at the beginning.
I still sometimes have to use a heating pad or very strong pain relief medication...but less now as my routine above is helping.

Tegretol, like all the antiseizure drugs, can cause brain fog. I'm having some of it too, but it is worth it for the improvement in pain.

Wishing you well...I know this is very hard!!!