If my son was arrested for assault when he was attacked by a man, can my son file assault charges on him?

He can make a complaint with the cops. Only DAs can file criminal charges.

Yes, but the prosecutor does not have to accept them. He better get an attorney and claim self defense.

The police make the reports and forward it to the prosecutor's office. It is solely up to the prosecutor on whether or not to press charges and whom to press charges against. If your son was attacked, he could raise the claim of self-defense. There is also the option of suing the other man in civil court. Make sure your son is represented by an experienced criminal defense attorney.