Yes, you can be arrested and charged for fighting: there is no legal right or privilege to fight. Even if the other girl hit you first, if you kept fighting her past any need to defend yourself, that is illegal: self-defense stops once you no longer need to defend yourself.Example: she punched you, then tried to punch you again; you hit her first to stop the second punch, then stopped hitting her when she backed off--this self defense and you did not commit a crime.But say she hit you once, then did not punch you again, but you hit her to "teach her a lesson" or in revenge; or you initially started defending yourself, but then continued fighting once you could have stopped--that is not self defense, but is  crime.