I broke my arm and now I can't open my right hand. Is there something wrong with my nerves?

Could be stiff joint. If you have not been moving all your fingers and wrist, they may have gotten stiff. If you can still fully move the fingers with your other hand, could be from nerve injury.
Broken arm. Could definitely be a nerve problem and you should get it checked out asap. Many nerve problems are avoidable or treatable i.E a cast might be too tight or there is a hematoma (blood) pressing on a nerve that can be drained. Or maybe the fracture needs to be treated differently. Best of luck.