You will need to be evaluated further to know for sure if a hernia is causing your shortness of breath. All of this could be sorted out by following the advice that you have been given to go to the Cleveland Clinic. However if you prefer a gastroenterologist in your area would be the type of specialist to check everything first as far as your stomach.
A hiatal hernia can crowd the chest area giving the lungs less room to work. Eating smaller meals can help since a full stomach also crowds the lungs causing increased shortness of breath. In addition to shortness of breath, this could cause the pain right in the middle of your chest and back. Often this is worse with any movement that would cause you to bend forward at the waist since it further crowds your lungs into a smaller space.