Ohio Department of Health keeps Covid-19 vaccine records.

[Buckeye_Democrat]

https://www.ohiopublichealthreporting.info/Enrollment/FileSystem/HL7/Public_Instructions_to_access_ImpactSIIS_record.pdf
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COVID-19 vaccine providers in Ohio are required to report patient information into the ImpactSIIS system
when the COVID-19 vaccine is administered. If you have received the COVID-19 vaccine in Ohio, your
information should be in the system.
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I mention this because the clerical worker at the local pharmacy where I was vaccinated obviously didn't know about it. She struck me as a Trump-cultist, and she acted angry when I asked her about my Covid-19 vaccines being shared with Ohio. "It's protected by HIPAA, sir!" and "The government can't confirm or deny if you've been vaccinated!"

The pharmacists and the MD who administered the shots were much brighter and nicer, at least.

Edit:
After seeing that uneducated woman's attitude about it, I created an online account with that pharmacy (a national chain) to verify that they had my Covid-19 vaccines recorded. They do.
And it was an MD who gave me the shots each time, based on the "prescription" information given to me each time it was done. I expected a pharmacist instead, but it was an actual medical doctor who administered the shots for me. The paperwork provided the address of her office too.