I am a Registered Nurse, however have never worked in Cardiac. That said, I want to give you my thoughts. The above comment is not entirely accurate. As for cardiac pain, it is possible to happen when resting, not exclusively during exercise, when one has coronary heart disease. The pain may well be muscular in origin, but with your significant family history, I would take no chances and call your doctor today to at least speak with the nurse to have her triage your symptoms. Your doctor may say it is ok to wait until your scheduled visit, or they may want to see you sooner.
Best of luck to you!
When you're talking about chest pain and SOB the day AFTER exercise, a musculoskeletal cause pops into my head. When I have a rib out of place, I can feel extremely short of breath and have a good deal of chest pain, completely non-cardiac in nature. Often it is a new exercise that brings it on. I did some twisting yesterday and I'm paying for it in the ribs and shoulder today, hurts to even breathe deeply *sigh*
Cardiac pain usually manifests while you're in motion, not when you rest - unless it's present both during activity AND at rest. Push ups are a prime factor in chest pain that is musculoskeletal, by the way.
Certainly if your pain continues or is accompanied by other symptoms, don't hesitate to get it looked into. But your age, clean bill of health and recent push-ups tell me it's likely not your heart.
I think it is great that you're taking measures to improve your health picture :) Hang in there.