Facial Pain from Invisalign?

It looks like there's a lot of pressure on your tooth at the second series. Your doctor is checking your tooth for any premature contact , or check the X-ray for PDL. The space between tooth and bone-widening. If the tooth is under a lot of pressure, an occlusal adjustment or change of your treatment plan is required.

There are many causes for nonspecific facial pain and they can arise at any time. If you were susceptible to developing trigeminal neuralgia it would likely have occured with or without the Invisalign.
Some people have underlying (asymptomatic) TMJ problems that cause facial pain as well and these too can become symptomatic at anytime, stress, trauma, bite problems like a deep bite, any type of dental work, tooth movement too.
You were likely predisposed to the problem, and it was coincidence that the TN started at the same time.
Have you worked with the Trigeminal neuralgia association? They are a great resource. You may also want to seek out a Dentist who does neuromuscular TMJ therapy because some of the symptoms of TN are very similar to TMJ and you may get some relief with orthotic therapy.