HS rules, known as NFHS, state that the penalty for the technical foul is two FTs PLUS possession of the ball for a throw-in from the division line opposite the table.
So, yes, the officials in your game were correct to award FOUR FTs with the lane clear to your opponents AND then administer a throw-in at midcourt to that same team. However, they made a slight mistake in the administration order. Under NFHS rules the FTs should have been shot in the order in which the fouls occurred. Therefore, the 2 FTs by the player who was fouled in the act of shooting should have been taken first, then anyone from the offended team may attempt the two free throws for the technical foul. This is a minor thing however and there is even a casebook play which says that a mistake in the administration sequence is not a correctable error as long as all of the merited FTs were awarded.
So you were incorrect and the officials were right.
Good of you to have the courage to ask and find out. Now you learned something.
However, under NCAA rules, technical FTs for unsporting conduct are administered immediately and then the game resumes at the point of interruption. That is what you were thinking should have been done in your contest.
In a college game, the officials would have administered the two FTs for the T right away with the lane spaces unoccupied, then would have lined everyone up along the lane and shot the 2FTs for the shooting foul as normal. In college, possession of the ball is not part of the penalty for most technical fouls. (There are a few special cases in which the team does get the ball as well.)