This doesn't really sound like a heart issue. I think you need to have a serious workup by a regular MD, rather than just a heart guy.
There are a lot--a LOT--of causes of back pain, all the way from musculoskeletal problems, like cracked ribs or costochondritis, to disorders of certain soft organs deep in the belly. An internist should be able to do what's called a differential diagnosis and figure out the source of your pain.
First, think about what you were doing when the pain first started: e.g., did it just start? or were you lifting or doing something physically hard? Just some ideas.
I can't associate a pain in the back with heart problems, but the shortness of breath I can. Have you measured you heart rate? does the pulse seem regular, no extra or missing beats? What is your blood pressure, you can measure free at any drug store, including Walmart. If you gave us some of those numbers we might be better able to relate to your condition.
When you say hospital visit, I assume you are talking about the emergency department (room) - did they do an xray of your chest? Did they do an EKG - surely they took your blood pressure and measured you heart rate, listening to it. Did they comment at all about these observations? If not, then there must not have been anything there seriously outside the normal.