Maybe you could show that one a scar, use the visual to help you with the words. Just say something simple like, "I self-harm after tests if I don't feel I do well". Maybe ask that one if they could be around after the next test, meet you at the door or maybe find your friends who are getting help and go with them and discuss the test to let off steam instead of self-harming, etc.?

I don't know the relationship between how well you end up doing versus how you feel you did right after? I would see if I could work with my tutor to make it more a "game" to see if you can get X score (and make it reasonable) and then the two of you look at or wait for the score together? If you usually get 92% or something, set the hope-for for the minimum, 90% and then you will usually be pleasantly surprised?