Either the goalie takes a free kick, or the opposing team gets a free kick at the goal.
Retake the goal kick
If by goal box you mean goal area, a box 6 yards from the goal. Then Yes, a goal may be scored within the box. EXCEPT: A goal cannot be scored on yourself from a goal kick or free kick awarded with in the your own goal area. If the ball is kicked from a goal kick or free kick awared with in your own goal area and enters your own goal the proper restart is a goal kick as the ball must leave the pentaly area to be in play. FIFA Laws of the Game.
The "little box" in front of the goal mouth is the goal area. There is no rule governing the goalkeeper and the goal box except that if the keeper is taking a goal kick, the ball must be placed on or within the lines of the goal box to restart play. (Note that the keeper or any of his teammates may take the goal kick - there is no mandate that the keeper take the goal kick.) Following the taking of the goal kick, the ball is considered not to be in play until it crosses out of the associated penalty area, which is the "big box" inside which the defending goalkeeper my use his hands to play the ball according to the Laws of the Game. It is highly unlikely that these rules are modified in high school soccer. It could be fairly said that the sole purpose of the goal area is to define the area from inside which the ball is to be placed in the taking of a goal kick on that restart of play.
You cannot score an own-goal directly from an indirect free kick or even a direct free kick. If the kick was taken from inside the kicker's penalty area and did not exit the penalty area before exiting the field, then the restart would be a rekick. If the kick was taken from outside kicker's penalty area or left the penalty area before exiting the field, then the restart would be a corner kick for the attacking team
During active play any player may kick the ball while inside the goal area.
If a foul is committed inside the goal area then it is also inside the penalty area. Any foul normally punishable by a direct free kick that is committed inside the penalty area by the defense is changed to a penalty kick.
The correct restart is a kick-off from the centre spot, to be taken by the team who conceded the goal.
The match is restarted with a kick-off after a goal.
During any goal kick the ball must be placed somewhere within the goal area. Any offense for which the restart is a direct or indirect free kick, then the ball is placed at the top of the goal area (6 yards from goal line) directly out from where the offense occurred. Please note that a penalty kick is an entirely different restart from direct or indirect free kicks. There is a persistent myth about a rule where attackers cannot enter the goal area during active play. It is untrue. Obviously, there are some restrictions during penalty kicks or kicks from the mark.
The ball position is all that matters.
If the ball is taking in to or kicked in to the goal area by the attacking side and the defending player touches it down in that area, or if the ball continues to move out of the in goal area and goes dead then the defending team will be allowed to restart the game with a 22 drop out.
A goal kick is performed when the ball completely exits the field across the goal line, last touched by an attacker, and outside the goal posts or above the cross bar (i.e. not a goal). The ball is placed anywhere in the goal area and is kicked by the defense to restart. The ball may not be touched by any player until it has exited the penalty area.