Can you press charges on an individual, 24 hours after an incident?
Did not previously want to.
You should be able to do this. 24 hours is not terribly long, especially for a victim who was injured in the event. But 24 hours is often the point at which the window of opportunity, as a practical matter if nothing else, starts closing quickly.
I'm assuming that in your previous contact with the police, you did not say anything that was not consistent with the accusation that you now want to make. If the fact is otherwise, you have a problem, because the inconsistency weakens your credibility, with law enforcement at the outset (including the prosecutor's office, which makes the final decision whether or not the charges you want pressed actually do go forward), and with a jury if the case goes to a trial in which the defendant has to be proved guilty beyond a reasonable doubt.
Similar reasoning comes up just from the fact of delay, and the strength of the argument increases with the length of the delay. If the defendant really did what you say, his lawyer will ask, why did you wait?