NFHS 9-3-6 : When a strikeout involves more than one batter, it is charged to the one who received at least two strikes. If no batter received more than one strike, it is charged to the batter who received the third strike.
I couldn't locate anything in either the NFHS Rules or Case Book regarding a change of pitchers during an at-bat, but have always told coaches to charge the first pitcher with the walk if he had thrown more than one ball.
While many of my fellow umps don't care about the score-keeping rules, I feel it only adds to our credibility if we do. Things such as catcher's obstruction being scored as an E-2 but not a time at bat and runner being hit by a batted ball being scored as a single come to mind.
While posting this, my demented mind recalled a happening from several years ago that you might enjoy......
SCENE : Runners at 1st & 2nd , 2 out. Grounder toward SS deflects off runner heading toward 3rd right into the SS glove. SS flips toward 2nd for the potential -but unneeded - force play...
(1) I announced : "Third out was caused by runner being hit by batted ball. Score the SS with a putout and batter with a base hit."
(2) The coach of the team at bat (always a screamer

) replied: "Auh, I don't care about that stuff.

"
(3) A fan, probably the batter's grandfather, leaped to his feet and screamed : "COACH, YOU @#$%&*^ BETTER CARE, THAT WOULD MAKE BUBBA TW0 FOR TWO

!"
(4) The coach looked at me

with a sly grin. I ,in turn, nodded

. I had unintentionally created an UMPIRE'S PAYBACK

!