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A painkiller was a medicine that eased one's pain.
Doctor Beverly Crusher gave Jean-Luc Picard a painkiller when he was experiencing an unknown form of pain when DaiMon Bok returned his previous command starship, the USS Stargazer. (TNG: "The Battle")
After Jadzia Dax was injured by a Jem'Hadar weapon on Soukara in 2374, Worf gave her painkillers, although the anticoagulant from the Dominion weapon meant she needed to take more. (DS9: "Change of Heart")