ANSWER:

This depends on the doctor. If he says that this is an illness that requires breaking off the fast, then so be it. But if he says that this is nothing and that it will go away after some time, then it is prohibited. 

Sheikh if some1 is suffering from intense dry,hard and rough cough so much that he needs water to stop it,in this case can a fast be broken because water was the need at that time and without water it can’t be stop or it can get prolonged