It is good to move your fingers after surgery, this prevents adhesions within the carpal tunnel and stiffness later.
If your fingers are puffy, then you probably aren't using your fingers enough.
If the base of your palm is puffy and sore, you might be doing a bit too much.
Your bandage is designed to minimise bruising and bleeding, so it can be removed after 24 hours. Most dressings on the palm fall off in the tropics, because the sweat will lift most glues. You can apply any dressing that sticks to your skin. Water proof dressings tend to hold the sweat in, and cause a moist wound. Water pervious dressings don't work well in the shower!
Orthopaedic Surgeon in Cairns, Far North Queensland