They would probably try starting you on something else first, then if it didn't improve may be more willing to rx something else. Unless you have a history of GERD (the title says you do anyways) or a history of actually trying other medications then that would bbe a good thing, but if not it would not be the first line of defense. It would not be the first choice out the gate. If you do though and have been on other rxes the that doctor would a lot more likely willing to try something else or even take a patient suggestion about a specific med although most docs don't like patients driving the ship on treatment and self prescribe something, for this it is not as risky as asking for something like say a benzo by name or something like that. It doesn't hurt to try whatever you decide to see if it works though, you'd just lose whatever time it was to get an appointment and go to it and you wouldn't know for sure unless you tried. Worth a shot but set your expectations to not get it and don't put faith in it being that easy. It could be, worth trying, there's nothing to lose by trying right?
I encourage you to do some searching on the site as plenty of folks have also asked this same question and it may give you a better idea of what others have tried, how successful (or not) they were and you can be better armed with info before trying. Nothing to lose by doing a little more research on it!
Best of luck and I hope you find everything you are looking for and get peace & serenity.