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Well, a common reason for burning and tingling in the hand, with pain in the wrist could be an issue called "carpal tunnel syndrome", which can come from compression of the nerve in the wrist area.
This is very common, and starting with a wrist splint to help keep the wrist straight can be done.
Other potential issues could be an actual wrist issue - e.g. arthritis. It can be referred pain, or pain in the wrist because of an issue somewhere else, most commonly a "pinched" nerve in the neck area.
It probably would be helpful to get referred to an orthopedic specialist, who can help to evaluate all three of these possibilities above, and help in further evaluation to get a diagnosis.
I have had carpal tunnel syndrome surgery on both wrists back in the 70's, I thought it was a one time problem. I do have arthritis and fibromyalgia also.
Well, what can happen with time is arthritis in the wrist and scar tissue from surgery can act to cause further compression of the nerve, so that may be what is happening in your case.
But it very well could be an issue in the neck as well, as it is fairly common for an issue at C6 - cervical bone #6 - to cause pain which can involve the wrist and the hand. A MRI of the cervical spine can help to evaluate this.