It could be something called a GERD cough. Is the cough like a constant clearing of the throat?
GERD is heartburn and not all patients actually feel symptoms of heartburn but only suffer from this mysterious cough.
Because I am not a physician only a Medical Assistant I can give you treatment advice. However, try some OTC (over the counter) medications for heartburn for 2-3 weeks and see if that helps. Prior to trying anything always consult your physician to make sure that it is safe for you to take.
Do you have any allergies to pollen, etc? Sometimes these will cause the constant coughing.
myrtle and cocoa helps. Just make sure it's actually young myrtle and mid-aged cocoa.