Severe facial pain for 4 mos, diagnosis of sinus probs & toothache. Currently have severe facial swelling. Could this be trigeminal neuralgia?

Dangerous condition. Severe facial swelling is not found with trigeminal neuralgia. This is likely caused by an infected (abcessed) tooth. Infection in the head and neck region is a serious condition. You should seek medical/dental care immediately.
More likely other. Those symptoms do not sound like trigeminal neuralgia. I would be more concerned about a sinus infection or deep dental infection. You should be seen soon to get the right diagnosis and proper therapy.
No. No, but potentially a serious problem. I would start with an exam by an oral & maxillofacial surgeon NOW. Toothache pain can be caused by sinusitis and vv. Severe facial swelling more likely with dental infection.
No. Trigeminal neuralgia is not associated with facial swelling. The pain is sharp and stabbing and not dull or aching. Pain and swelling usually point to some type of an infection. Sinus infections don't usually cause facial swelling. You most likely have a dental infection. You should see a dentist for a proper diagnosis and treatment.