It's not entirely involuntary--but yes, difficult. Not impossible.
What you've got is essentially soreness from repetitive movement, the same sort of thing that people get when they make the same movement on the job day after day. To get it to go away, the best thing is not to stress those exact same areas, either to move less or move in different ways.
Braces may help--not too tight, just enough so that your wrists aren't constantly moving. Just a little bit of support, and perhaps a reminder not to flap so hard. Or change the movement just a little, so that you're not putting stress on your joints in the same way. Try holding up your hands and bouncing instead of flapping them vigorously for example, or moving your hands in different ways.
You need not wear wrist braces constantly; many people with repetitive movement injuries find that wearing them just at night helps. That way your wrists are held steady at night to heal.
If you are still sore after a couple of weeks, you should probably ask a doctor. Most likely s/he will just prescribe a brace and not so much handflapping, possibly plus a wrist rest for when you use your mouse and keyboard... But still, if it's not healing, it's safest to ask.