Is there any correlation or association between having gastroparesis and the symptom of shortness of breath?

Not directly.: When you're bloated from gastroparesis, the abdominal distention reduces diaphragmatic excursion during inhalation, so perhaps indirectly you may feel short of breath if you're distended in the abdomen.

Gastroparesis: Not commonly. Gastroparesis is known to cause symptoms such as nausea, vomiting, early satiety (feeling full after eating just a few bites), abdominal bloating or abdominal pain, and in some cases a loss of appetite. Shortness of breath is an uncommon symptoms but may be related to other comorbid conditions.

Indirectly: Gastroparesis can lead to a distended stomach which can create a sensation of shortness of breath but this wouldn't reflect true lung or heart disorders. A different situation would be either gerd or laryngopharyngeal reflux which can irritate the larynx and cause shortness of breath as well as coughing.