Is it okay to "correctively train" a soldier and post it on social media?

Maybe on the puking, no on recording and posting.
Whether someone pukes or not has too many variables to give a hard yes/ no answer. I'd be more worried about dehydration then the fact a Troop Puked. I always figured if I didn't do dumb shit then I wouldn't get corrective training. Knowing the standard, meeting the standard resulted in no one bothering me.
The purpose of corrective training should be to correct an issue and dissuade repeat offences not embarrass or shame a Soldier.

Uhh...jaw gapes and rocks slowly back and forth on its hinges, then abruptly falls to the floor in disbelief....

That’s gonna be a hard “no”