Ah... so that's how he got hurt. Shinji can see how this might have happened, even if Kyoko's reaction sounds extreme at best.

With his free hand, he reaches over to delicately pat Kai's icy, icy hands. You did well, but please don't get hurt like this. "That was important for you to do," don't say that like it helped nobody. "I can't say I'm happy that it happened, but... I'm glad you could stop her from hurting herself."