To find which nerve relays pain from the ethmoid sinus, follow the sensory supply of the air cells back to its parent trunk.
The ethmoid cells receive the anterior and posterior ethmoidal nerves. Both of these are direct branches of the nasociliary nerve, a branch of the ophthalmic division of the trigeminal nerve. So any painful stimulus from ethmoiditis is conveyed through the ethmoidal nerves into the nasociliary nerve.
The distractors supply other territories: the frontal nerve handles the forehead and frontal sinus, the lacrimal nerve serves the lacrimal gland and lateral upper lid, and the infraorbital nerve from the maxillary division covers the maxillary sinus, cheek and upper lip. None of these innervate the ethmoid cells.
Hence the nasociliary nerve is the carrier of ethmoid sinus pain.
\[\boxed{\text{Nasociliary nerve}}\]