I could be wrong here, but from what I've heard, shin splints are essentially muscle tissue cramping along the length of your shin. So there isn't much "healing" done by resting. Apparently they come from increasing mileage too quickly. Start back in more slowly, increasing weekly mileage regularly, but in small increments. You might be in great cardiovascular health, but your legs need to ease in.
As for the forearm splints, I feel you.