First of all, Ohio doesn't have permits, we have licenses. Subtle difference, but still worth clarifying.
Secondly, how do you own your handguns if you don't mind me asking? Reason I ask is because in Ohio, you can't legally purchase one until 21. You can still legally possess one at 18, so I was just curious.
Finally, there is no laws concerning open carry. Until earlier this year when wording was adopted stating that localities cannot legislate against open carry. Assuming it's legal to possess the handgun (sounds like it in your case), you may carry it openly. Just keep in mind that ALL open carriers are subject to harrassment, including by police. If you don't have a license to back it up, some, less educated police will hassle you more. Being under 21, even less educated (or more zealous) police will hassle you more. If you accept this risk (and I hope you do both out of lack of fear and ability to educate them), then you should be in the clear.
Of course, our Second Amendment says laws be damned; For as long as you're not hurting anybody unprovokedly, you are legal to keep and bear arms.