Do I lack sympathy?

So when my son whom is 9 years old gets hurt he carries on and exaggerates quite a bit. I mean I am very sympathetic for the first 20 mins but then when the screaming and crying doesn’t stop after that I admit I start to feel a little annoyed and anxious especially when I know his “owie” isn’t as bad as he’s playing it out to be.

Tonight he slipped on the stairs coming down to ask me something well after I had already put him to bed. He got a fair bit of rug burn up his back and screamed bloody murder for at least an hour, he begged me to keep him home from

School tomorrow and told me he would never be able to sleep again with his back hurting so bad. I checked his back out and made sure nothing else was hurt and it was just in fact rug burn that was bothering him and then after an hour of him crying I told him he needed to stop carrying on even tho it hurt he had to be brace as there was no magic trick to make the pain stop. I told him to lay down and try to sleep, and that I was going to leave his room and come back and check on him in a half hour.

Was that cold of me? Should I not have told him to stop crying? I felt bad but really there’s nothing else I can do. How do you handle your kids who really overreact when they get hurt?