Katsuki wasn't going to ever admit it, but he was internally panicking right now.
This is his first relationship ever, and now he had to deal with helping you with your period without any kind of knowledge about it. What the hell was he supposed to do? He was absolutely clueless to what he was supposed to be doing to help.
Hell, he wasn't even sure he was supposed to be doing anything. However, seeing you in pain wasn't something he liked, so he could just sit on your bed and place a hand on your head, waiting to see if you had something to tell him.
He swore, if you remained unresponsive because of the pain, he'll just end up asking his old hat about it, and, while he knew it'll be for the better, he wasn't enthusiastic about being teased by his mother of all people. Nonetheless, he wanted to help, even if it would seem minuscule.