Whenever I hear someone compare forearm pain to shin splints, it makes me think of tennis elbow (basically, tendinitis). The symptoms of tennis elbow are not just relegated to pain above or behind the elbow. It can also cause pain down the forearms too. A simple test is trying to pick up a can of something from the top with your hand. If you feel discomfort in your forearms, it could very likely be that form of tendinitis.
I'm not a doctor or anything, so get it checked by someone who can tell you what's going on. If it is tendinitis, stretching your wrists (especially in the downward position gently for at least 30 sec. x 3) will help. Ice after workouts will help too. If it hurts lots while you workout, then stop.
Aggravating this type of tendinitis will definitely cause a very long recovery... trust me!