Can a hiatal hernia cause constant shortness of breath?

Yes: Hiatal hernia is a mechanical reason for shortness of breath. Depending on how big it is and how much of a mechanical disruption is there surgery may be warranted.

Unlikely: Some can get quite large or para esophageal and compress some lung, but i would seek another explanation. Smoking inhalation high altitude heart disease anemia etc.

Hiatal hernia: Yes it can if it is large enough. Should be evaluated with a ct-scan and surgery is indicated. But in a 28 y/o unlikely to be that big to cause such symptoms. Reflux is also associated with a hiatal hernia and that can cause irritation of the airways if bad enough that can manifest as a chronic cough.