I fell and hurt my hand. I had an x-ray, which showed no fracture. But I still have a terrible pain. What can I do?

Repeat X-ray. On occasion, hairline fractures may not be initially visible on the first set of films but may take more time to become apparent on a second set of xrays obtained a week later. Otherwise rest, ice, compression, elevation and nsaids may be your best friends if recommended and not contra-indicated.
Depends. X-rays show bones and their relationship to each other. An x-ray will not show crushed tissue, though it will show swelling. Swelling makes nerves send pain signals to the brain. Pain medication (anti-inflammatories) will help, as will elevation, immobilization and resting the hand. If not sure what was injured, go see your local hand surgeon for expert evaluation, make sure ligaments are ok.