Many (all?) states have an immunization registry ("Immunization Information System"); when you’re vaccinated, the provider submits a digital record with your name and date of birth, along with their info and the vaccine info, to the registry. This is programmatically ingested by Epic’s EMR system, if configured, and will even show up in your mobile app and web interface when logged into your health system’s app. So, in some cases, yes.

With that said, for emergencies, one might have an emergency bracelet with this info on it in the event pain management is required unexpectedly. Otherwise, pain might not be managed.

https://www.cdc.gov/iis/contacts-locate-records/index.html