1. Speak to your doctor. Listen to them over anyone else. If that isn't available, then you can:
2. Ease off on the activity. Do it less. This gives your body some time to heal.
3. Change your environment so that the activity puts less stress on your wrist. Eg if your mouse hand's wrist hurts due to using the mouse then you can lower you sensitivity by a lot (4x). This will force you to use your entire arm to move the mouse around instead of the wrist and will make it easier on the wrist. You could also get a vertical mouse or change keybinds around. If your keyboard hand hurts then getting a mouse with lots of programmable buttons can be helpful. Changing where your mouse and keyboard are in relation to where you sit can help (move them closer, further, higher, lower). The idea is to just change it so that other parts of the body take some of the stress.
4. Once you've healed enough, you should start exercising that part of the body slowly to make it stronger. Stretches at first and move on from there.
Step 3 is the easiest way to notice a big difference. I went from my mouse hand's wrist hurting within a few hours to having no issues even after an entire day by just lowering my mouse sensitivity.
I believe there is something to do with the way I use my thumb. I will try to change which thumb I use to hit space bar. Will require some getting used to, though...