There must be some sort of system that shares info some of the time. I signed up for a new doctor (haven't even visited yet) across the country from my old one,

There must be some sort of system that shares info some of the time. I signed up for a new doctor (haven't even visited yet) across the country from my old one, and the website of my new doctor's medical center already knows all my historical vaccine dates. I didn't give any of that information over, just my name, birthday, and SSN.