What is the likelihood of having shortness of breath and cough from hiatal hernia?

Possible: In general a hiatal hernia would not cause these symptoms but if you have a large hiatal hernia and you are refluxing from it and aspirating chronically it could definitely cause shortness of breath and cough. This can eventually lead to serious pulmonary problems. Get checked out by your local health care provider. It is treatable.

Could be: Cough and shortness of breath can be caused by many things, but a hiatal hernia can cause them by allowing stomach fluids to reflux into the esophagus and upper airway. However if you are severe shortness of breath you should seek medical attention right away.