Hi, This may be Trigeminal neuralgia as you have typical one sided facial pain extending to temple and eye( ophthalmic branch
of trigeminal nerve may be involved) and sore gums
of the teeth
of same side (maxillary branch
of 5th nerve). Trigeminal neuralgia may have a triggering factor like recent history of tooth extraction, touch, cold breeze or hot sensation etc. which you need to evaluate and avoid.