The correct answer is: Maxillary division of trigeminal

The trigeminal nerve is the nerve that supplies sensory innervation to the skin of the face. It has 3 divisions. The maxillary division of trigeminal (V₂) is the one that's important for this case--it is a sensory branch of the trigeminal that provides innervation to the skin of the cheek, upper lip, lower eyelid, and the lateral portion of the nose. This is exactly the area that the patient feels pain, so it is the correct answer. The ophthalmic division (V₁) is a sensory nerve that passes through the superior orbital fissure and supplies sensory innervation to the eyeball, conjunctiva, nasal mucosa, medial portion of the nose, upper eyelid, forehead, and scalp. The mandibular division (V₃) is a sensory and motor nerve--it supplies skin of the lower lip, chin and lower jaw. V₃ also provides motor innervation to the muscles of mastication, tensor veli palatini, mylohyoid, the anterior belly of the digastric, and tensor tympani.

The facial nerve innervates the muscles of facial expression, but it does not provide sensory innervation to the skin of the face. The glossopharyngeal nerve provides sensory innervation to the pharynx and sensory and taste innervation to the posterior 1/3 of the tongue. But, it does not innervate any skin on the face.