Whenever my daughter would have public displays of big emotions I'd try to remind myself of a few important things:

First, that my child has a right to feel her feelings and to express herself in the language currently available to her without being judged by me or anyone else. That this is an opportunity to develop her language around feelings and coping with them. And that it is a good thing she feels safe enough to show those feelings to me.

Second, when my brother and I were small children and decided to display our "big emotions" we did so in a packed grocery store, after our mother's card was declined, and banshee screamed that our mother was trying to "kill us" because we were obviously going to starve to death. My mother carried two children (doing our very best to be wailing dead weight) out of that store under each arm. Thanks to a genetic condition, my brother's nose had a logic defying ability to cover him and anything in his vicinity in an ungodly amount of blood whenever he was upset. So, my mother left that store with two children insisting she was trying to "kill" them and re-entered to clean up two children sniffling and covered in blood. If she could handle that situation and still shop at the same grocery store (CPS was called, for obvious reasons), I can handle whatever thoughts passing strangers had about my daughter's behavior.