Usually Trigeminal Neuralgia is caused from a blood vessel pushing on the trigeminal nerve. As far as I know, the only way to diagnose it is through history. It can be caused from dental procedures. I have Atypical Trigeminal with severe pain behind left eye, burning in left side of nose, and pain along upper gum area. I have no sinus promblems however, other than NO mucous at all in my nose. What other symtoms do you have?
Sinusitis can indeed be a cause of this problem, as can a tooth abscess. I would suggest getting a CT of the sinuses to evaluate these symptoms.