I can tell you from first hand experience about this kind of pain. I had pains on the left and right side of my body, I was diagnosed with GB disease and my gall bladder was removed.Not too long after I began to get the pains on my left side of my body still. It was terrible, I couldn't take deep breaths, lie down, or move much at all without getting sharp stabbing pains that I thought were going to kill me. Sometimes it'd even happen in my sleep and wake me. A year later I was diagnosed with MVP and I also have mitral regurgitation. Although they can't necessarily trace the pains mvp may cause certain people, I started beta blockers and I haven't had the pains since. I only take 5mg of it a day and that seems to do the trick. They relax the heart so palpitations become less likely and so there will be less regurgitation because the heart isn't stressing as much and the mitral valves are suppose to be strengthened. I just know my pains have gone away. Hope this helps.
The gall bladder is on the right side of the body so it most likely isn't that. I have MVP and at times at get a sharp stabbing pain on the left side right under my nipple area and I attribute it to the MVP. I You should check with your cardio or primary care physician.
What you have described could also be caused by reflux.