The pain you're feeling is not associated with heart pain. Heart pain feels like a weird sort of crushing sensation, and radiates along your chest, shoulder and jaw. What you're describing is pain in your chest wall muscles. I used to do the same thing after I started trying to exercise more.
But really, what you're feeling is soreness from the exercise. Everyone who exercises gets those same sensations. its just that those of us with anxiety issues tend to freak out about things, on a hair-trigger. And chest pain is really good at inducing anxiety.
in short: I wouldn't worry about it.