When I lay down it feels like something heavy is laying on the right side of my chest. What could it be?

Several things. Chest pressure could be a heart symptom such as palpitations or coronary disease. It could also be a musculoskeletal issue or even a lung problem. Speak to your physician to ensure its nothing serious.
Chest wall strain. This is most likely chest wall strain due to physical or emotional stress -- but you need to see your doctor anyway and get yourself evaluated properly.