mold and mildew
Cleansing and diet will definitely help, but it sounds like there are environmental issues that MUST be dealt with, too.
My husband developed a similar cough while working in a very enclosed, overcrowded office. When I visited, it reminded me of childhood vacations and my grandmother's dank, musty, moldy old basement. Nothing we did seemed to help the cough until he found another job. Once he wasn't exposed to the mold and mildew anymore, his cough cleared up fairly rapidly.
Call in a mold inspection professional to do some mold tests; make sure they check behind baseboards and sink cabinets and in the walls and ceilings, not just on the surface. If you can't find any in the local yellow pages, call a few local building inspectors and ask for mold specialists. And you may want to see about retro fitting some form of ventilation. Often it can be done for under $100 - well worth it to help remove the humidity that mold and mildew love.
Good luck!