She’s referring to the HIPAA release and/or medical power of attorney. It is most important for the agent – that’s YOU – to have the “paperwork” on your phone. You are the one who will be calling the ER and saying, that’s my son you’ve got there, I’m his designated agent, and I can email you the signed paperwork to prove it.
What your son filled out at his pediatrician’s office is just for that office.