After falling on right side, wrist is swollen and very sore. Can still move fingers etc. Used ice to

if the wrist hurts to move or is sore at end ranges then yes, immediately immobilize the wrist with a brace because you may have sprained it. continue icing. if it doesn't feel better in about half a week see a doctor or physical therapist. nsaids like naproxen, or ibprophen are good to take as well.