You didn’t hurt your little self, did you?
"little" implies the person is physically/really young(little)
younger than the other speaker?
I feel a sort of feeling that the speaker is taking a pity on the person whom s/he speaks to.
While the statement might be appropriately used to a very small child, to an older child or an adult it would be offensive. It would be taken as implying the immaturity of the hearer, and might also imply that the injury was so minor that only a very small child would take notice of it.
In these days when we are encouraged not to talk down to people of any age I would never use it.