Congrats.
In Ohio you can go in anywhere within 30 days before your 21st birthday and get an over 21 style license. They make it instantly, you might have to wait 3 minutes for the machine to crank it out if they're busy.
Once you have that Over 21 license you're golden because no one actually checks the license, they just look at what type it is. The under 21 licenses are either horizontal or vertical (depending on when you got it) and are red and white. They say "Under 21 until XX/XX/XX in bright red on the front. The over 21 are white and yellow, printed horizontal. Since they're so easy to tell apart, I guess no one wants to take the time to read the actual birthdate on it.