Welcome at HCM.
Arthritic hand is less flexible & is more prone for injury.
If after fall down there is no fracture
or bony injury on x ray then there can be ligamentous injury or strain to the wrist.This will relieved by giving it rest & avoiding heavy work for few days.
You should take a good analgesic
for few days.
You should also consult to your orthopedic doctor for this.
Hope this will help you.
With best wishes.