It seems that you have had a ligament tear of the wrist due to fall.
There are various ligaments of the knee that are very susceptible to sprain and tear due to excessive shearing force. They derive nutrition from the synovial fluids around the joint and hence do not heal very soon. Ligament sprain usually require conservative treatment whereas excessive deformity can require surgery.
I would recommend the following-
1)Consult your physician and obtain a X-ray of the wrist. This will help to determine if there is any gross deformity or trauma like fracture. X ray doesn't help to diagnose ligament pathology.
2)Consult an orthopedician and discuss the need for an MRI of the wrist. MRI shows any pathology of the wrist and aids in its diagnosis.
3)If it is a sprain, you will need complete bed rest for about a week and then you will have to restrict your physical activity. Ice packs and cold compress will reduce the inflammation.
4)Take Tab Tylenol 500 mg to reduce the irritation or swelling, if there's any.