What could be the cause of my chronic cough? (it is not asthma, gerd, post nasal drip or any of the other typical problems)

Many things: Many diseases could cause those symptoms including viral, bacterial and fungal infections, sarcoidosis, wegener's granulomatosis, malignancy, rheumatoid arthritis, lupus, churg-strauss vasculitis, etc. You should see your doctor to begin a work up.

Chronic cough: Medications is another cause. Have you been trialed on meds for the cough such as an anti-reflux pill for 4-6 weeks or an inhaled medication for 4-6 weeks since much of reflux is silent and there is a large component of something called cough variant asthma with totally normal breathing tests.