Have a real good look at the total picture, not just your wrists.

Getting a new chair is one thing, but that doesn't mean that it is the right chair for you.

There are people that specialize in this sort of thing, maybe you can find one in your environment ? There are so many factors to consider that you'd be studying for weeks if not months to figure out exactly what is going on here.

Hardly any of these symptoms is 'single cause', and like debugging any problem that has multiple interrelated parts it's going to be hard to break it down into items that can be fixed individually.

It's really good to see you take this serious, don't ever ignore those warning signs. And that dull, persistent numbness is a good indicator that you have a very serious problem, as long as that persists I'd avoid that keyboard/screen/desk/chair setup like the plague unless you absolutely have to.

And find a doctor that will get you referred to someone that can have a good look at your wrists.