What can cause severe pain in right side only under the ribs right under your breast, it hurts to cough, sneeze, lay down, and breath?

Not the heart. : A number of issues--outside in: broken rib, muscle strain, pleurisy, pleural fluid, pneumonia, pulmonary embolus (blood clot), etc. If this is still occurring, hopefully you have seen your doctor and gotten at least a chest x-ray. Should be treated if still there.

Sounds mechanical: It sounds like you may have a mechanical chest wall problem such as costochondritis. You should get in to see your doctor to ruke out more serious reasons for chest wall pain though. Your primary care physician can take a good history and do an examination.