If my boyfriend broke my skull and I didn’t see a doctor or report to the police, what will happen?

If you had a skull fracture and did not see a physician you are crazy. So I assume the injury was much less serious. You can still report the assault and battery to the police; the longer you wait the less trustworthy the police will think as to your report. If you are still with that person, you are crazy, since if he intentionally hit you, no matter how much he may have apologized afterward, he will do it again. You are putting your health in grave danger.