Such pain is often caused by a musculoskeletal disorder or nerve compression/inflammation. If accompanied by tenderness, it is almost always muscular. In that case you should make a careful inventory of the physical activities you engaged in, prior to the onset of the pain.
If it seems to wrap around your chest from back to front, it is likely to be a problem with one or more of the nerves between the ribs, called intercostal nerves. Other causes include gastroesophageal reflux, with "heart-burn". The pain could also be due to a viral pleurisy, sometimes called, "The Devil's Grip" or pleurisy due to clots to the lungs.
The EKG is a good sign but not a guarantee that the pain is not coming from your heart. However the continuous nature of it and the lack of an association with exercise would be atypical for coronary artery disease. You may have to have further testing.
Bottom line is that this is most likely a benign pain and will resolve spontaneously, over time.
...it's just a thought but ...the nerves coming from your c-spine (neck) supply from facial to pectorial muscle areas (as well as other) ...i have had problems with this ...some of the pains in pecks are obvious that they are the actual muscle justing ...but sometimes it feels more vague as to where its located (like a chest pain?)
...maybe this is why it is not always on the same side??? ...if discs in your neck (or other prob?) move... i am not medically trained, just been through a lot with musculoskeletal problems...
until God heels us, wishing you His best