Yes, it could be acid reflux. Trouble swallowing and trouble breathing are two symptoms of bad acid reflux, according to my doctor. I've had both, though the breathing trouble was very slight and it only appeared once, for a few days, after I'd skipped my evening dose of medication for a couple days.
But I don't know about your other condition, so I wouldn't know if those are symptoms of that. But maybe your doctor would consider having you take something like Prevacid, and see if that relieves your swallowing and breathing problems. I was on Prilosec and then Nexium for awhile, but my GERD gradually overpowered both of those, so now I'm on Prevacid. The Prevacid is pretty expensive, but it's worth it to me because now that I'm on it I have absolutely no symptoms from the acid reflux, thank goodness.