I think Steven adressed this in one of his blog entries. Icing will constrict the blood vessals, thereby lessening the amount of blood that is going to the area where the ice is applied. This is why ice brings down swelling. Ice can be used as part of the recovery process, which is where you'd want to use it. Try going 20 minutes with ice, followed by 20 with heat, repeating 2 or 3 times.
Advil can be helpful after throwing, because it has anti-inflammatory properties.