There are a few of us who also have wrist problems from time to time. First question, when you cube how many solves do you do in one sitting? Do you take breaks during a cubing sessions, or just do a bunch of solves in a row for an hour or more?
I have problems with my wrist as well, and they always appear whenever I do about 100 solves in one sitting. If I do about 100 solves or more in a single sitting, without taking any breaks, I've learned that I have to ice my wrist and forearm, as well as take it easy the next day and not cube as much. I've learned to take breaks, and break up my cubing into sessions that are spread out throughout the day rather than all at once.
Sadly, my wrist problems have not gone away, I've only learned better how to deal with them. Definitely ice your wrist if you feel soreness or twinges of pain. Definitely don't cube at ALL for the next 3 days if you feel twinges of pain. If you feel soreness, then take it easy the next day and do maybe half the solves you did the first day.
Try doing some BLD solves, or an FMC solve whenever your wrist starts to bug you. Try just plain stopping for an hour if your wrist bugs you. You can also buy one of those carpal tunnel wrist supports if your wrist bugs you really bad, and wear that if you ever feel sharp pains in your wrist.
Basically, the problem will probably not go away. You will have to learn to deal with it, and don't expect to go back to the "normal" way you used to cube. You need to create a new normal way of cubing that doesn't bother your wrist. That way you will still be able to continue to practice without making your wrist problems worse.
Lastly, and this probably goes without saying, make sure you use a relatively good cube (not too loose, this makes wrist problems WAY worse), and also make sure to lube the cube if it is locky. Locky cubes hurt my wrist more than non-locky cubes. Super loose cubes are the WORST possible thing for your wrist issues. Try tuning your cubes a little bit tighter and see if that helps.