Just wanted to chip in and share my experiences with GERD and breathing issues as I have had these for 30 years - on and off an hope that what I share can help.
I get really bad reflux at times particularly at night. When this happens, apparently the inflammation from the stomach and the esophagus spreads to the diaphram as well as the lungs themselves. So all of a sudden you get spasms in the diaphram which makes you feel like you need to keep taking a breath even though you know you must be breathing OK because you haven't collapsed. Often this is worse at night simply because the acid is creeping up due to your prone position although you may not necessarily actually feel this. Then the lungs themselves can cause this "air hunger" because the little lung sacs tighten up particularly if you have breathed in some of the reflux acid and this causes that horrid breathless feeling. Sometimes the severity of the feeling of breathlessnes can be quite scary and as a result you can then feel anxious - this of course will make the feeling of breathlessnes even worse like a vicious circle.
GERD is not necessarily all that easy to manage and you need to be proactive about it. I tend to manage mine with diet and a raised bed head and sleep on my left side (the right side or on your back can make the reflux worse) because the various medications available all seem to give me side effects and I am allergic to anesthesia so surgery to fix the hiatus hernia is not exactly an option for me. Also I avoid bending or lifting anything heavy and watch my posture and sitting postition - any time you "squish" your stomach you will be pressing together inflammed tissues that will hurt plus you will squeeze the acid upwards which is the last thing you want.
In terms of the breathlessness - many years ago a friend gave me an "incentive spirometer" which is a plastic thing with three balls where you have to suck air throught the tubes to raise the balls. Normally these are given to patients after surgery to improve their lung function. I find that if I am starting to get anxious about my breathing I use the spirometer to "prove" to myself that I can breath and my lungs are OK and the anxiety dissipates. This might be a useful tool to help.
Just in terms of the GERD - when I have a particularly bad case - I use the cabbage juice cure which works a treat and is better than taking nasty drugs. Just google "cabbage juice GERD" and you should come up with a heap of info on it.
Also the other thing that I find that helps is breathing exercises. I do QiGung breathing exercies which give me a fairly instant positive response - however there are all sorts out there - just google "GERD breathing exercises".
Remember that everyone who has acid reflux (or GERD if it is chronic) will have a different set of ancilliary symptoms and some of these can potentially be quite serious. So it is important to get your reflux under control plus avoid the unpleasant pain and discomfort that comes with the territory.