I'm sorry man, you've got to be 21 to buy a pistol in most places along with at least 3 business days waiting (not including weekends, it is not cool). You are close!!
In FL, I believe you can buy a pistol at age 20 if you buy from a private seller locally but have to be 21 to get one in a shop. Good luck!!

No you can not purchase the firearm as it is federal law that you must be 21 years of age to won a handgun, and it is also federal law that in any state in order to buy a handgun you must be a resident of that state. Therefore since your a resident of Ohio and not Tennessee you cannot purchase the handgun. You can buy longuns in any state no matter your state of residence. Hope this helps

To buy a handgun in Tennessee you must be a resident and also 21 to buy from a licensed person or entity. Unfortunately as an Ohio resident and also being under 21, I believe you would be unable to purchase a pistol in TN.