A cat that suddenly coughs and then gets better may be caused by hair balls in the body, choking on drinking water, or catching a cold. First, check whether the cat is in low spirits, sneezing, or has a runny nose, etc. If there is, then it is a cold and the cat needs to be given pet cold medicine; if there is not, then you can feed the cat some hair removal cream or cat grass to help the cat expel hairballs from the body and prevent the cat from getting hairball syndrome.