i'm pretty sure i cracked a rib last year during a mud run, from falling off an obstacle. i was actually sure that i broke it that day, but the symptoms lined up more with just a crack and a bruised lung.
i took a full month off of exercise at first, doing little more than taking the occasional walk. once i was able to breathe well again, and move easier, i upped the pace and added in a little light cycling. after about two months i found that i could handle some light jogging, hiking, etc...and i could manage a pull up with minimal pain. from there, i would try a little more each day, increasing my pull up and push up numbers/difficulty.
i've tried working through injuries before, and i've tried resting to heal. resting wins without a doubt.take some time to heal and come back strong. resting allows the body to do it's thing and send blood where it needs to go, your ribs, rather than trying to refill you legs or something from working out.