I believe you should discontinue all medicines for a week or two to get rid of any residual traces of medicines in your body. The two causes you are mentioning are treatable. Going by GERD
keep bowel clean avoid irritants have small amount of food at frequent intervals and herbal medicines like kamdugdha ras soot shekhar ras swarn yukat avipatikar churan.
or post. nasal drop can be cured with mahalakshami vilas ras swarn yukat and swamla.
these are the medicines to strike at the root cause but your symptoms of cough
need locally acting herbs first and for that sy. crux and sucking of kanth sudharak vati offer excellent relief.