There is another possibility regarding pain on deep breathing. If you are just a couple of weeks post-op, it could be that your lungs are not yet fully inflating. Don't forget that they deflate your lungs while you are on the heart-lung machine during surgery. They do this to get extra room to work. Since the lungs are moist on the inside, sometimes they stick to themselves and do not fully inflate once you start breathing on your own again. I had pain on deep breathing after surgery and this was the diagnosis. I think they were able to see something on my chest X-ray to confirm that diagnosis. The treatment was ibuprofen, along with continued heavy use of my spirometer. After a few weeks, it all just cleared up.
Oh - They told me that most of the tissue that was cut and worked on during surgery (especially the heart) does not have pain-sensor nerves to cause post-op pain. Only the muscle and tendons, etc. have pain sensors (along, of course, with all of the skin and body parts closer to the surface).