It would help to know how you and other caregivers respond to the crying now so we can throw out some new ideas.

With my oldest, I used to make the distinction between crying and wailing. Crying was allowed but wailing generally was not. It cut down on the performative stuff and was also less obnoxious to bystanders. To my mind crying is like normal genuine tears, wailing is where the people in the next exam room can hear you after your shots. Crying got him sympathy and hugs from me, wailing (outside of a major injury) got him in trouble.