It totally does NOT scream carpal tunnel syndrome to me.
I think they maybe bough on by your art related activities. Technical stuff + stress = excessive tension --> joints and muscle dysfunction??
Left hand: I would suggest you to research on "alexander technique" application to "pain problems".
I'm thinking maybe there is excessive tension in the wrist flexor & extensor muscles when you are using your hand, causing unnecessary force through your wrist. A simple way I could think of: keep left hand totally relaxed and move it with your right hand alone in the same way you described that usually cause your grinding/popping symptom. If there is no/minimal symptom when the movement is performed passively by right hand, then my assumption is correct. However, it doesn't mean there is absolutely nothing wrong with the wrist joint and tendons, just that they could be secondary symptom caused by muscle imbalance, (or could have some unusual/ serious problem underneath which need further investigation, but don't worry too much just yet).
Right hand: It sounds like tendon problem, but pain is not reliable. What you feel may not be what its actually happening. You should get it checked out by orthopaedic Dr, and physiotherapist. They are most capable at dealing with pain problems. In my opinion, you should get it checked out, make sure there isn't any radioulnar joint ( within forearm) problem, or any other serious causes. Once that's done, physiotherapist can work on the tendons with you.
Treatment will be divided into three parts:
1) Relieve inflammation ( Ultrasound, Ice)
2) Reduce tightness (Stretching)
3) Increase elasticity/loading capacity of tendons (Eccentric loading exercise, with weight)
The most important thing is to learn when to increase weight for the exercise. Progress too early will set you back big time, or even worse than before. You really need hands on session with you therapist to work out a safe loading weight to use.
Don't forget to mention your Left hand problem to your therapist while you're at it.
From what I know, "alexander technique" is not part of physio training, and its not common either. So don't be surprised if they haven't heard of it. You'll have more luck searching for videos in youtube. Once you understand the core concepts, you can apply it as many way as you could imagine. Its really very good, a life long skill.
All the best!