Criminal law violations are offenses against the state, not the individuals. So, whether the two of you combatants "wanted to press charges on the other" does not determine whether either or both of you will be charged with criminal law violations.
Your participation in the court proceedings may be compelled unless you have a valid reason to oppose orders of the court.
You likely should stop discussing the details of your case with anyone, including your parents, except your attorney. Other people may not have any basis to not testify to what you tell the persons.
Given your age, you may end up either in juvenile court or adult court depending on where the prosecutor wants to prosecute and whether the judge agrees.
The prosecuting attorney is the only one with the authority to press criminal charges and ultimatley this is the person that decides whether or not to charge you with a crime. The wishes of the "vicitms" or the opinion of the school may have some infuence on the prosecutor's decision, but usually very little. If police are involved, and they forward information about the incident to the prosecutor, it is likely that you will both be charged, regardless of your wishes.
It is very hard to prosecute cases of mutual combat or where the witnesses are not cooperative. Do not contact the prosecutor or try to talk your way out of the situation. Anything you say can and WILL be used against you. Get a good attorney that knows how to fight these cases, and talk to the attorney before you discuss this case with the police, prosecutor, juvenile probation, or anyone else, or you could very likely find yourself charged and convicted of assualt.