Can a hiatal hernia or GERD cause heart symptoms and difficulty breathing?

Yes. A hiatal hernia and gerd can cause chest pain and palpitations. A large hiatal hernia can cause shortness of breath by crowding your chest cavity and limiting expansion of your lungs.
Yes: see doctor! Severe symptoms such as these indicate a need for surgical repair if medicines aren't working. A surgeon with expertise in reflux disease should get involved for appropriate work up and possible surgery. Severe reflux can lead to a variety of serious problems if not treated. Hiatal hernias should be carefully evaluated to investigate the possibility of a paraesophageal hernia- may be serious.