Sounds like either gas pains or an inflammation of the cartledge that connects your ribs to your sternum. Have you tried Prilosec, Zantac and watching your diet? Also, have you tried an anti-inflammatory such as Motrin? Hope this helps.
When you press down on your chest you can not exert enough force to depress the heart or have any effect on the heart with your own pressure. Your rib cage protects your heart from blunt force trauma. See another doctor, a cardiologist. Ask for a echo cardiogram, non invasive sound test.. Good Luck..