Anyhoo, I've noticed that my hands have been sore the morning after.
The amount of comments that could be made about finding a girlfriend really makes me wish I hadn't imposed that PG-13 rule...
As for warmups and cool downs, it really just sounds like you're hitting the thing too hard, or you're being to tense when you play and holding the tightness in your hands too much.
My warmups have nothing to do with getting my hands ready. I'll always play along (unplugged) with the last song or two played by the warmup band, just to start feeling it. Otherwise, 20 pushups and I'm ready to go.