One of the simplest, and quite difficult, mindfulness exercises I have seen bhikkhus recommend is not to scratch when you have an itch. Most itches go away on their own in a minute or two. If it’s caused by something more persistent, like a bacterial or fungal infection, scratching can worsen or spread the infection, and might wipe away any medicated cream/ointment you may be using. Of course, you still might want to look at the itch, in case it’s caused by something like heavy sweat or an insect on your body, which perhaps you should remove.
Similarly about coughing… both otolaryngologist (ear, nose, and throat (ENT)) and internist doctors have told me that coughing is hard on the throat, and that it’s usually better to drink liquids to clear the throat.