I don't hunt if I am seriously ill. I begin to halucinate when fever hits about 102 degrees. I do have allergy issue that commonly results in coughing. I have a cough muffler - you know, one of those things you cough into and it works like a firearms silencer. It works OK but is not perfect. Also, mentho-lyptus cough drops are just as vital to my hunting kit as my bow and quiver. As soon as I get in the woods I start sucking on a cough drop and don't stop till I get back to the truck. Also, if its a bad enough cough that I need to use a potent cough medication, I hunt on the ground. Otherwise I get groggy and clumsier than usual.
One other thought on coughing. If you take blood pressure medication, check on side effects. I was taking lycinopril and it caused a chronic cough that would make you think I was a heavy smoker. I changed off and the cough cleared up in a few days.