Hand pain? Need help ?

If it was broken, it would be extremely swollen and discolored. You wouldn't be able to use it at all.

You just landed on one hand a little harder or at a different angle than the other. Since you only have minor swelling and pain, that means you have a sprained wrist, bruised bone, or a hairline fracture. None require medical attention. Take advil or aleve, whichever works better for you. Get a wrist brace from any pharmacy. The foam ones that lace up are the best. They provide the most support, protect from impact, and can be adjusted to fit your arm exactly without putting pressure on the wrist. Avoid anything with elastic because those hinder blood flow. They're better than nothing, but not the best solution. Take it easy using that wrist for now.

In the future, while training or practicing, get a pair or wrist braces from the athletic section of any sports store. Near the rollerblades, there are tiny wrist braces designed for impact with pavement. They're small pieces of metal on the palm and top of the hand with elastic on the sides to keep them aligned properly. Elastic at this point isn't a problem because it's a preventative measure instead of something to treat an injury. They're small enough to stay out of the way, and tough enough to protect your wrists. (I wear them for roller hockey, and I've been thrown to the pavement tons of times. They work really well.)