Hi Dan, I am sorry you are experiencing pain.Here are a couple of suggestions for you.
1. Did you have any injury to your wrists that may have precipitated this pain?
2. How are your wrists feeling and looking at this time?
The reason for asking this is obvious: I would be worried about a joint injury and a subsequent infection. It does not seem very likely though from what you are describing, but is still worth investigating.
Next:
1. Are both of your wrists involved? Any other joints that are bothering you?
If that is a yes, I would be looking into an autoimmune process, such as rheumatoid arthritis (RA). In fact, I would encourage you to bee seen by a competent rheumatologist, as treating RA early and aggressively is imperative to prevent joint damage, which is usually irreversible. The current guideline is to be seen and evaluated by a rheumatologist within 2 months of the onset of symptoms.
Finally, sore throat could be a coincidence or related. If it is related, I would recommend being tested for certain infections, among which is syphilis.
These are just a few things to investigate. Hope you find some answers. Let me know how it goes.
Have you been tested for Lyme's?