As a general principle of law, statutes of limitation require that suit be filed within a certain number of years from the incident giving rise to the lawsuit.
Unless the parties to the dispute have agreed to "toll" (extend) the limitations period during their settlement negotiations, which means that the defendant has agreed not to raise the expiration of the statute of limitations as an affirmative defense to the plaintiff's lawsuit, the statute of limitations will generally bar (prevent) the plaintiff's suit after its expiration, even if the parties were negotiating.
"Filing a claim" means filing a lawsuit in a court which has jurisdiction to hear the matter. "Filing a claim" does not mean "filing a claim" with the defendant or its insurance company.
Not legal advice as I don't practice law in Ohio. It's just my two cents on the facts you describe in light of general principles of law. If you need legal advice, please consult a lawyer who holds Ohio licensure. That's not me.
You may be out of luck I am sorry to say. In Georgia, the applicable statute of limitations is two years. The claim could have been preserved had you filed a lawsuit. The rules in each state differ so you should contact a local attorney as soon as possible to find out if your claim is now barred.
The statute of limitations here requires that you file a lawsuit with the court within two years of your injury. Unfortunately, filing a claim with the grocery store is not enough to preserve your claim under Ohio's statute of limitations.