Hello rc998,
Is it a boney type of soreness or a skin type of soreness? If it is boney then it might be a costochondritis type of tenderness, it does sound a bit like it to me. Basically it is inflammation of the ribs, and hurts like heck when pressed like you describe.
There is a lot of information about this condition on the internet. I would advise you to research it and then obviously you can decide whether it is something you think you need to go to see your doctor about. Please don't worry, I personally do not think it is heart related. I say that as I have had 2 heart attacks and a triple bypass, and my heart attacks did not present with that type of pain at all. I am not medically trained, just talking from my own experience.
Hope this helps.
goldenwings