My left hand aches when I'm doing chest work. I finally figured out why, but this probably won't help you: I injured the palm of my hand several years ago - sliced DEEP into the muscle in the fleshy part of the palm at the base of the thumb. That's exactly where my hand aches, and it's only the hand that was injured - my right hand never aches at all.
So, unless you've ever had hand injuries, this might not be the same problem you're having.