Can someone file for a complaint 3 months after the crime?

Heres what essentially happened. Something happened at school, where i hurt another student. The aftermath of my decision was a red mark with minimal blistering on the persons arm. A week after this happened, his arm got a SMALL burn mark BARELY noticeable (even to the victim). The parents of the student called the police, but ONLY REQUESTED THEY HAVE A TALK WITH ME. And the deputy told me that "A report was not even made (to go to the DA),they only wanted me to talk to you." The deupty had a talk with me, and he understood that my intent was not to harm, but to only joke around. Can the parents go back and file for a complaint 3 months after this happened? If they decide to go back and file for a complaint, will this Red mark with blisters, qualify for "Great Bodily Injury?"