Aristocrates, did I see in another post that you mentioned your diet? And that perhaps it isn't full of whole fresh foods. Perhaps you can look at what and how you are eating to explore that cough. You may have a food allergy and I agree medication is not necessarily the best way to deal with that, but you should do something. Perhaps you could see a nutritionist, or read up on whole foods. Getting that brown guck out, whatever it is, out of your system should be a priority!
Best, D