A flute player to whom I give occasional Jazz lessons wrote that she had over-practised and now has pains in her hands. She also wrote that she needs to avoid driving, to aid recovery.
One more thing to think about: if driving is bad then I wonder if you have an issue with gripping the wheel. Meaning perhaps you grip the wheel far harder than you need, and perhaps you do the same with the flute.
In the car, you can practise just relaxing your hands. When playing, there’s an exercise where you just rest your fingers on the keys, and then blow. You then gradually increase finger pressure until the sound is correct. You need press no harder than this. The pressure required will vary depending on how hard you are blowing. This idea applies just as much to stringed instruments.
Many guitar players press far too hard. You’re squeezing the neck, guys. It won’t improve your sound, it will slow you down, and you’ll get RSI.