"a violent, noisy effort to expel air from the lungs," early 14c., coughen, probably in Old English but not recorded, from Proto-Germanic *kokh-(source also of Middle Dutch kochen, Middle High German kuchen), with the rough "kh" of German or of Scottish loch. Onomatopoeic. Related: Coughed; coughing.
As a noun from c. 1300, "single act of coughing." As "illness or other condition that affects the sufferer with frequent coughs or fits of coughing," by 1742. Cough-drops attested by 1829; cough-medicine by 1828. To cough up "to present, hand over" is from 1894.