Really annoying cough

[SW_Pat]

My thinking is that this is part of acid reflux, but I'm here because I'm really not sure. I've been having heartburn, fullness, throat-clearing, etc. But this cough sucks. It's throughout the day, not really fits, I'll cough a handful of times and then be done with it for a bit. But it tastes absolutely terrible. And sometimes, not every time, there'll be a slight wheeze after I've done it. It feels like it comes from the top of my chest / bottom of my throat. I'm just wondering if this is sort of par for the course with acid reflux and/or what I can do to get rid of it.

Thanks!

Edit: just want to add that the bad taste also occurred when I sneezed. It doesn't happen every time, but enough. Would really appreciate any response. Thanks again.