咳嗽[gaisou] coughing
含嗽薬[gansouyaku] gargle medicine
嗽ぐ[kuchisusugu] to gargle

含嗽剤[gansouzai] mouthwash
嗽薬[ugaigusuri] mouthwash

漱ぐ[yusugu] to rinse
枕流漱石[chinryuusouseki] sore loser stubbornly refusing to admit being wrong and adhering to the far-fetched argument
漱石枕流[sousekichinryuu] sore loser stubbornly refusing to admit being wrong and adhering to the far-fetched argument

盥漱[kansou] washing one's hands and rinsing one's mouth
石に漱ぎ流れに枕す[ishinikuchisusuginagarenimakurasu] refusing to admit being wrong and adhering to the far-fetched argument
漱ぐ[kuchisusugu] to gargle