When you are sleep-deprived and your baby is screaming, you need a short list, not a research paper. Here is what works:
Acetaminophen or ibuprofen (6+ months). These are the most effective tools you have. Do not feel guilty about using them. You are managing legitimate pain. Dose by weight, follow the timing guidelines, and give proactively (before bed, before naps) rather than waiting for the crisis.
Cold items. Chilled teething ring (refrigerator, not freezer). Cold wet washcloth (twist it, chill it, let them gnaw). Chilled spoon pressed on the gum. Frozen breast milk in a mesh feeder (6+ months). The cold reduces inflammation and provides numbing.
Pressure. Your clean finger pressed firmly on the sore spot. A solid teething toy designed for chewing. A cold washcloth with a knot to bite on. Counter-pressure on the gum modulates the pain signal.
Comfort. Holding, rocking, skin-to-skin, singing, white noise. Your baby is in pain and scared because they do not understand what is happening. Your presence is a genuine form of relief.
Distraction. For older babies and toddlers: new toys, bath time, going outside, music, books. Distraction does not eliminate pain but it competes with it for attention. A baby absorbed in a new activity hurts less than a baby with nothing to focus on except their gums.