Sick player

[Little Jimmy]

USSSA rules (all rule sets welcome). I'm in the field. Pitcher is getting rocked on a very warm day. Each hit takes its toll on her and at some point she looks like she really is ill. She waves for coach who comes out with Mother and gives her an inhaler. After a moment or so of using it, she hands it back to mom who walks away with coach. In my judgement, nothing has changed. Pitcher is woozy, shaking her head, starting to cry. I say to coach she still doesn't look right, but he just waves me off with mom just shaking her head next to him. Just when I think I need to interject myself more, pitcher drops to her knees bringing out coach/mom and finally she is replaced.

My question is did I even have rule to back me if I felt that this illness merited the withdrawal of the player? This wasn't concussion oriented and for a moment I thought that I needed to do something. But would I be overstepping my authority? Anything to back me?