Thanks, CHfather, for that wealth of info!
No, my PCP didn't prescribe anything for TN—in fact, he seemed reluctant to do so. He suggested I keep a journal of my supposed TN attacks/circumstances/triggers, etc., as he did for periodic bouts of vertigo in recent months, which seemed to have stopped as of this month (of course, that brings me to another question—whether any CH sufferers have also had problems with vertigo). He did mention antiseizure meds as a possibility for the future, though, if the TN was bad enough.
As a result of the vertigo I was experiencing, my PCP ordered a CAT