Best Answer: Yes the drainage can cause persistant coughing, but also it may be developing into bronchitis.Have you tried the medicine Mucinex? If you have high blood pressure you must be very careful with taking any decongestants. Best suggestion is to make an appointment to see your Doctor. GERD gastroesophegeal reflux disease can also present as drainage, but actually is excessive acid backing up into your throat that feels and appears just like sinus drainage. Again, only your Doctor can determine.