If herpes can cause vestibular neuritis. Is it possible it could spread throughout the nerves causing things like trigeminal neuralgia?

No, See Neurologist. The most commonly accepted theory of what causes trigeminal neuralgia is vascular compression and not viral infection. See a neurologist or orofacial pain specialist for final diagnosis.
Probably not. H simplex type-1 typically causes infections of oral mucosa &establishes a lifelong persistence in sensory ganglia . Persistence and latency have been demonstrated in human trigeminal, facial, and vestibular ganglia. The reactivation of virus in ganglia generally causes cranial nerve disorders such as herpes labialis, Bell’s palsy, and vestibular Neuritis. No evidence of trigeminal neuralgia.