Exercises. No, seriously. I have a lot of chronic pain issues, particularly in my entire right arm/wrist/hand, and that was what was told to me.
But also, ergonomics.
Here, let me show you something that I wish more people would know about:
This is a vertical mouse.
Most people use a normal flat mouse, or they try to use a touchpad on their laptop, or something like that. Those things are exactly something that contributes to the very problem you're talking about.
Think about it: If you just lay your arm on a table, while you're seated there, and just let it naturally rest, your hand will not be laying flat, it'll be on its side. But to use a normal mouse, you must TWIST your wrist to do so, and hold it in that position. The entire time.
I use that specific mouse in the photo there. And WOW did that help.
I'll put it this way... you think your hand/wrist problem is bad? Mine got so bad a number of years back that I literally could not HOLD a mouse. At all. For a period of about... a year, I think it was... I used a game controller to emulate the mouse, because I couldnt hold a real one. This was exactly as bad as it sounds. Once I COULD hold one again, I learned about the vertical mouse, immediately bought one, and... yeah. Talk about a difference. No way I'd ever go back to a classic mouse.
But also, there's other aspects too. Like elbow position and whatnot. Pain you feel in your hand, shakiness and weakness, that isnt always IN your hand. It could be in your freaking shoulder. This nonsense travels (experienced that one myself).
None of this should stop you from drawing or something like that. I mean mine got so bad I was taking 4 Advil every 4 hours. For months. But, it's gotten much better, and now I'm drawing. You can get to that point too, but you gotta put in the work, as I had to. Exercises, positioning, activity time monitoring, using ice or whatever if something happens that seems like it might cause inflammation (I haaaaaaaaate using ice myself, but I will say, it does work).
And that's a hard fact, when it comes to physical problems of the sort that might be approached with physical therapy: you either put in the effort, or A: nothing happens, or B: it gets worse.
My advice: First, talk to a doctor, seek treatment. See what they advise. Ask if a brace might help as well. I use an arm brace, this armband thing. I always wear it. Worn correctly, it... does something. My physical therapist explained to me like 12 times just HOW it works and why it works, but I never quite grasped it. All I know is that it works, though it took time getting used to it.
Sitting around telling yourself how bad it is though, aint gonna do anything at all. Except maybe make it easier for option B to happen. And trust me, you do NOT want option B to happen. I cant stress enough just how painful that is.
Also I want to point out that the thing with the mouse, I'm not saying that JUST the mouse is the problem or the thing to fix. Look for other things in your day to day life that may be potential causes, and make adjustments. You'd be surprised, just what kinds of things can affect you in this specific way.