Combine peaches, sugar, lemon pulp and juice, orange pulp and juice, and water in a large mixing bowl, stirring until sugar dissolves.
Pour mixture into freezer can of a 1-gallon hand - turned or electric freezer. Freeze according to manufacturer's instructions 15 minutes or until mixture thickens.
Beat egg white (at room temperature) until stiff peaks form; fold into peach mixture. Continue to freeze according to manufacturer's instructions. Let ripen at least 1 hour before serving. Scoop into sherbet dishes, and serve immediately.