I finally went to a doctor today. Overall, good news.
Minor rotator cuff damage in my left shoulder
Possibly a couple of broken ribs on my right side
He suggested x-rays for the ribs, but as he admitted, it is kind of pointless since they can't treat it. I really don't like getting x-rays, especially of the chest. So we didn't do any x-rays.
Anyways, it just needs some time.
Who knows how I injured both sides of my body? I don't remember the actual fall. My first memory is of me lying on my left side, but somehow my right side took a beating too.