if I'm nervous my hands tend to get cold and tingle. Then my hands start to freeze and become hard to move, especially whenever I'm playing on the piano.
Can you record a video of yourself playing for someone to check if you're maneuvering your hands in a painful way? E.g., when your body gets stage fright, you might unintentionally bend your wrists up or down which might interfere with your tendons and blood vessels -- restricting blood flow or twinging nerves.
Even if the idea of recording a (small) performance makes your body stressed, remind yourself that you want to observe any physical oddities so that you can improve them.
Also, do you practice vocalizing your performance? I don't mean sing it, but rather get the pitches roughly correct but with good timing. I find that by vocalizing a piece first, you're teaching your brain how to perform it, which helps teach your body how to perform it as well.