I'm probably sure that the sacrifices aren't sound, but the psychological advantage is always enough. Also, if everything fails, you can just perpetual the other person's king after you stripped its defenses away.
It is a nice attacking game. The sacrifices are correct in the sense that it was the best you could do. You were 2 pawns down. After that both sides made mistakes in attack and defence, but in the end you won. Well done.