As we age, our tendons and muscles lose quite a bit of their natural elasticity, and become "stiffer" and less responsive than before. Each person is an individual case, but it happens to us all.
If there are NO OTHER side effects, such as numbness or prolonged pain, I would venture to say that this is the most likely culprit.
If, as you say, the problem is alleviated after just a few shots, you might be able to achieve some success by having one of the squeeze type "stress" balls or some other type device to help you loosen up your hand and forearm muscles prior to your leagues practice session.
By the way, what weight of ball are you using?
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"The difference between stupidity and genius is that genius has its limits."
Albert Einstein