If you can calm the GERD, the cough may go away (did for my sister).
I have a chronic cough (due to surgery that unfortunately rendered one vocal cord useless, so I have a particularly weak cough). It's really only bad when I have a lot of mucus, such as during a cold and for weeks after, and mostly when lying down, so what works for me may not work for you.
At any rate, if a cough drop doesn't help, I take a low dose of a codeine cough syrup with guaifenesin (brand name Cheratussin AC). It calms the tickle for me within minutes. My doc prescribes a bottle or two a year for me, but it's available "behind the counter" in some pharmacies in some states.
Another thing that an cause a chronic cough is an ACE inhibitor, generally prescribed for blood pressure. I would hope your doctor knows this, though.