@irisnicole8405 Nope. She does not need it!
In the event of an emergency, medical providers will provide life saving measures. For anything else, they can contact you directly.
The only reason she would be looking for that form is to do something without your knowledge. If she won't disclose whwn medications are given, that puts her at risk of being overdosed.
You are following ped advice and ahe is following her curve so that is all that matters. If she can't respect that, it may be time to find new child care.
(As for allergies, I have food sensitivities that didn't show up on testing. Regardless, it is still outside of grandma's role to badger when you have sought medical help).