Consider switching to the Wii U Pro Controller if you aren't using it. It's much easier on your hands than the Gamecube controller. Completely tournament acceptable.
The joysticks are much less stiff and pretty much all the buttons take less effort to press. Especially the shoulder buttons. I've played a ton of hours with both controllers, and can play for way longer with the pro controller. In my opinion it's miles easier on your hands and wrists.
Other than that, it's very important to rest from playing. Especially if you're experiencing numbness, that's a big sign you need to cut down on your play hours. What you're describing sounds like carpal tunnel, which is basically inflammation pressing down on the nerve in your hand, causing the numbness. Repetitive strain injuries will only get worse if ignored so definitely don't ignore it.
If you're on the computer a lot as well and your mouse hand is the one hurting, consider switching to a trackball mouse like this one:
http://www.amazon.com/Logitech-910-000806-Trackman-Marble-Mouse/dp/B001F42MKG/ref=sr_1_2?ie=UTF8&qid=1433913413&sr=8-2&keywords=trackball mouse
As someone who spends 5 days a week in front of a computer at work, that thing has done so much to save my wrists, I used to have a lot of pain. Also get a nice wrist pad for your keyboard. Oh and learn to use a mouse with your off hand, feels weird at first but you'll get used to it and it will make it so not one hand is bearing all the daily stress.
Also do the common sense stuff. Apply ice and heat. Look up exercises and massages you should be doing as well. Also, weight lifting regularly does wonders to strengthen your hands and wrists.
If it's really bad and doesn't go away in a few months, go see a doctor.
