Severe or persistent pain or swelling or a decline in your performance usually mean it's time to seek medical help. When tissue is damaged, fluid accumulates in the injured area, leading to swelling. Swelling will limit the motion of the joint and may contribute to pain if it gets bad enough. RICE therapy is important because swelling in an extremity is hard to reverse once it's been there awhile. It's best to prevent it in the first place.
Rest is essential to keep an injury from getting worse.
If you ignore the problem, you may continue to aggravate the tissue damage. This doesn't mean you have to stop completely. If the activity hurts, don't do it. If it doesn't hurt, continue. Ice or anything cold can effectively decrease pain from an injury.