Veginator, it sounds like you might have a separated rib - where the rib tears away from cartilage. I've had broken ribs, which prevented me from doing any exercise and took about 3 months to heal. Everything I did was excruciating. I've had a slightly separated rib once, and right now I believe I have a badly bruised rib from body conditioning that went a bit wrong at my kickboxing gym a couple of days ago (shin in ribs instead of abs). I'm in a lot of pain, but nothing seems to be moving around in there like it shouldn't, so I think it's bruising. Hurts like hell though and it's bringing back memories of my broken ribs.
There's not much you can do, except take ibuprofen (I prefer to just live with the pain) and try not to stretch or contort your ribcage. Get rest, take it easy. Bruised ribs should heal within 4 to 6 weeks, and you can probably find some exercises that don't hurt them. If your ribs are separated a bit, you have to move around a lot less, and they will take longer to heal. You should probably go to a doctor and get x-rays.
Rib injuries are really painful. I'm onto my 3rd one in 4 years.
The most frustrating thing is I'm missing kickboxing, BJJ practice and the rest of my training for a bit.
Oh yeah, while you're healing, be extra aware of how you modify your body movement to avoid pain. When my broken ribs were largely healed after 3 months, I had a very weak core and a bunch of back problems!
Good luck with your healing!