Can I protect a T-shirt design that has an acronym?

As long as the "Ohio acronym in which the words shape into the state of Ohio" is original to you, you can copyright the image-plus-acronym or any original graphics on the shirt. The protection will be somewhat narrow (mostly against very close adaptation or copying), since copyright is more easily worked around than other intellectual property protection, but it is still protection and it is inexpensive and easy to get--basically, just put the "c in a circle" copyright symbol next to it and, if you see anyone copying it, take steps (e.g. a cease and desist letter; lawsuit, if necessary) to stop them. (You have to actively protect copyright and other intellectual property.) Copyright is available for any original text and/or graphics.
If the image, etc. is distinctive and not similar to what anyone else has, you may be able to trademarke it, too, which is broader protection, but harder to get (more requirements than copyright) and which generally requires registration and therefore costs around $1,000 - $1,500 with legal help, though could apply yourself, without an attorney, and knock the cost down to around $350 - $400. The U.S. Patent and Trademark Office has good information on its website about trademarks and the process of applying for them. Note that you have to actually be using the would-be-trademark in commerce (i.e. selling the shirts) or about to, with a *final* design, before you can trademark.