When monitoring my kid's pitches, ultimately it's only about what I see from him and how he feels.
We try to get at least two sessions in per week in addition to the game he pitches in. Once he's loose and starts to throw with game intensity, I count every pitch, whether it occurs on the side, between innings from the mound, or in the game. It may seem like a lot but it racks up fast when you count them all. A league may have an 85 pitch limit and pat itself on the back for taking care of kids, but if the kid throws 40 before the game, 5 between each inning and goes at least 4 or 5 innings he's looking at 125-150 game intensity throws per outing (even if he doesn't throw hard with his between inning warm-ups). If he throws two bullpens over the course of the week and throws 15-20 to get loose and another 50-60 per session, now we're talking another 130 pitches on top of his 150 for a whopping 280 where the league reports only the 85.
I only allow my son to throw in one game per week, no matter how many games the team plays. I think the bullpens are far more important than the games for his development. At his age, whether or not the team wins is secondary because these teams are built for parity or as I say (parody).
In the bullpen, if I don't like something I see and he can't get it corrected in the next 2-3 pitches, we will cut it short. If he's throwing a lot of pitches in an inning and the defense isn't supporting him, I take him out early an rotate through other pitchers to keep fresh arms in there rather than wear anyone down.
So when I say he throws 250 pitches per week, it's total pitches and not 250 in a game in addition to the uncounted number that most coaches allow their kids to throw in warm up or on the side without any consideration.
My son has only had arm soreness twice in the 5 years he has been pitching, he was shut down on that pitch and the soreness did not linger beyond a few hours and certainly not overnight.
He has never thrown sore or in pain, yet he throws a ton of pitches.
After summer ball, he takes about 45 days off (mid July until sept 1) Then fall ball starts up and runs another 6-8 weeks. Then he doesn't pick up a ball again until February because he swims competitively during the winter.
During breaks from throwing, he's only taking batting practice and fields grounders and underhand or wrist-flipping the balls into a pile behind him (infield practice does not need to involve throws all the time by the way coaches). The hard part is fielding the ball. The throwing is easy, so why waste a kids arm throwing every grounder across the diamond to first? I never understood that.
All together he takes over 5 months off from pitching each year. He's the hardest throwing 13 year old there is in our eight town league, so I think it's working nicely and he throws about 5000-6000 total game intensity pitches a year. The league sees only 1800 of them.
Conversely, some kids throw only in games and are sore after 3 innings yet pitch in two games per week. They don't throw enough to keep their arms in shape. If they don't do the work on the side, they will never improve their game or their endurance. Guess what happens when a league gets too many sore arms? They reduce the pitch counts because that's the only thing they can control.