Concerto love, do not tie a ruler to your hand and do not try to make your wrist stiff or straight like that. The best thing is if you follow your teacher and ask your teacher for advice.
Cai hong's advice to do scales is not bad, but c.h. is still young, trying to help, but not experienced yet like a teacher. Being able to do things is like a journey: you get to play scales fast by first playing slowly, and eventually after days or weeks playing faster. Scales are not the simplest thing to do on the piano because there is so much to them - you move your hand into new positions, you have strong and weak fingers, what your thumb does etc. so take it slowly and get your teacher's advice.
What's probably happening is that when you try to play scales fast, all your fingers are trying to get ready at the same time so they all get tense. Your fingers have to learn to take turns, because if you make them all tense you get rigid fingers. What happened is probably normal. So slow down, speed up gradually and if the hand gets tense again, slow down and try again. But really, talk to your teacher.