If you are throwing in the cold wear plenty of layers and keep your arm warm. If your throw with just a T shirt on you'll pull several muscles in your arm and shoulders. Another was is to not throw so fast that throw your arm out. Before each game ice and heat it up. Use icey hot for example.
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The most important thing to do immediately after a game is to ice the arm. When it is not hurting, make sure to work on strengthening the entire arm (ask your coach or look on the internet for exercises to do). Another important thing to do is make sure you properly stretch and warm-up before each time you throw. The pain could also be caused by a poor throwing motion.