Unpire Struck / Live ot Dead Ball?

[rj]

High School Semi-Final game; 2-2 bottom of the sixth; 2 outs; 3-man; I'm 1st Base umpire. Runner on 2nd; 1st baseman playing just inside of 1st base; 2nd baseman is about ten feet left of 2nd and playing close to the outfield grass so she's forced me to be about six feet off her left shoulder a couple of steps further out. The batter rips a bullet line drive about four feet high straight at me; no chance to get out of the way and strikes me on the hip as I move left. Ball bounces towards first base at which time the 1st baseman picks it up and makes an errant throw to the plate so the winning run scores.
The defensive coach wants a dead-ball call but the three umpires get together and agree the ball passed an infielder other than the pitcher (in this case the 1st baseman) and there was no chance another fielder could make a play on the ball; therefore the ball is live and the run counts. The game was written-up in three local papers as ending on a controversial call.
Would love to hear veteran opinions.