I really don't want this Hedonism II forum to turn into a Covid testing forum, this is more for resort related items. We can talk more about the need to get tested for travel to Jamaica in the Jamaica Chat forum on this message board. But I will address this specific question here, then close the topic. It will be moved to the Jamaica Chat forum for any follow up. But the follow up will need to be limited to being tested in relation to traveling to Jamaica and not just testing in general.
From the 5-minutes of searching the internet for testing in Ohio, I found several references to places you can get tested even if you don't have symptoms and where they will write out a doctor's order for you on site. One reference I found is https://coronavirus.ohio.gov/static/MHSF/COVID-19-Ohio-Testing-FAQ.pdf.
If you Google: - where can I get tested for covid in Ohio - you'll get a lot of references to check. There are a lot more places than hospitals where you can get tested.