You're just lying or ignorant about what's available in your state. There's a website that you can put in your zip code, and find a place with times available and book that time. No need to 'scour' the internet - it's a one stop STATE-run website to make this step unnecessary.
gettheshot.coronavirus.ohio.gov
And the STATE held a bunch of MASS VACCINATION CLINICS across the state, had mobile vaccination clinics, and has a website that's a one-stop shop to get an appointment across a number of public and private vaccine providers. So the state was very involved from the beginning in holding people's hands, and it's because non-morons know making things easy increases how many people do those things. It's why doctors send you reminders, because prodding works. Etc.....
I don't know why you're so eager to prove one of three things 1) you are lying, or 2) are ignorant, or 3) both, all to make some stupid defense of what the wingnuts did in in Tennessee. And you can't keep your excuses straight.
1) The State of Tennessee didn't do vaccines or send out info or postcards!!!!
2) Oh, well, sure they did do all that and more, but the many vaccines the state DID administer didn't matter because free markets, and also reminders are useless, although the free market knows better than you and sends me a half dozen reminders for every appointment, because in the real world people forget, get busy, don't do what they are supposed to do when it comes to public health. Our vet sends us postcards to remind us to keep our dogs up to date on vaccines. My HVAC guy sends reminders. Dentist. Specialist. Volunteer coordinator. These are all necessary but one reminding people of the second shot are NOT!!
3) Ohio didn't do any of that, so when Tennessee ended those efforts it didn't matter because Ohio left you guys to fend for yourself.
4) Except for the MASS VACCINATION CLINICS the STATE held all across Ohio and the vaccines still being administered by local governments, and much more, etc..... - you pretend those didn't exist and don't still exist, when 1 minute on the Google proves you are wrong.
Why are you doing this? The wingnuts are running the healthcare show in Tennessee and it's stupid as hell, reckless, and has nothing to do with public health but instead with stroking the egos of idiots Q's and MAGAs who have believed a bunch of garbage being peddled to them by liars and idiots.