cough: [14] Although it is largely disguised by the modern English pronunciation, cough is of onomatopoeic origin. It came from a prehistoric Germanic base *kokh- (the kh pronounced not unlike the ch of loch), which initiated the sound of coughing. This has no recorded Old English descendant (although one probably existed, *cohhian), and first appears in the language as Middle English coughen.
early 14c., coughen, probably in Old English, but not recorded, from Proto-Germanic *kokh- (with the rough "kh" of German or of Scottish loch; cognates: Middle Dutch kochen, Middle High German kuchen). Onomatopoeic. Related: Coughed; coughing. As a noun from c. 1300.