What can cause a burning stinging pain in my injured wrist?

Nerves. When you injure your wrist it swells this puts pressure on the nerves to your wrist joint and can cause stinging or burning pain in the wrist. You need to have the wrist evaluated and appropriately treated. Pain is there to tell you to do something smart.
Need more info. There are many potentially injured structures; it's impossible to tell without examining you. For an idea of the possibilities go to www.Rearmyourselftexas.Com.