Yes Gerd can make you feel short of breath. I have had that when refluxing and it irritates the Vagus nerve. Felt at times like I couldn't catch my breath. It is not uncommon for that same situation to make people feel like they are having a heart attack. Until I got control of my reflux last year I had a couple of months of this. The Vagus nerve travels down near the esophagus and can be impacted by the acid and inflammation that occurs to it when your refluxing. It can be a circle, you feel this, it makes you anxious and it makes your stomach produce more acid causing more reflux and it can then feel worse. Have to break the cycle thru diet, meds, lifestyle changes.