The only thing that is at all concerning about rib injuries is; is it a costal cartilage injury? Costal cartilage is what connects your ribs to your breast bone, and to your vertebrae. Barring this kind of injury, you should be fine, outside of the pain. Good things about this kind of injury: very small chance of any long-term damage, debilitation tends to rely on pain tolerance, and it tends to heal relatively completely (again, barring a costal cartilage injury), simply due to the structure of the rib cage itself. Bad things about this injury: it can take a long time to heal completely (I've heard of particularly nasty soft tissue rib injuries take up to 3 months to heal), it's difficult to treat (simply not much you can do, other than take it easy on yourself and let it heal), and it's fairly easy to re-injure (especially when you use it, i.e. applying pressure with in whilst in side control, back mount, etc. then the guy bucks right into your ribs. OUCH!).
My advice: try to compete, but if it hurts too bad, then don't. Pretty simple. You'll know whether or not you can go. If it's not healed up enough, there's just no way your body will let you compete, there will be too much pain.