Can my case for being arrested for assault be charged for assault and battery?

Yes, it is possible for someone to be arrested on charge A, and the prosecuting authority decides to file a different charge after a review of the evidence believed to exist at that time. It doesn't take much contact at all to establish a battery in addition to an assault. If you do not already have counsel, it is time to obtain counsel. Few need counsel more than someone who is wrongfully accused.