I live in Ohio also and it is well settled law that one can be discharged without reason and NO private cause of action is viable unless one of the exceptions to "at will" employment can be articulated.
I don't see any from the Ohio case law I know of. I am of course eliminating federal and state laws concerning discharge under the guise of race, color, etc, since you do not claim it is because of that.
1. You did not blow the whistle (statutory whistleblower law)
2. You do no have a claim for Promissory estoppel.
3. You do not have a claim for a Public Policy exception. At one time Ohio did NOT recognize such, but the court later overruled itself.
The Ohio SC has laid out exceptions 2 and 3, BUT still adheres to the at will employment doctrine. The common law states any employment NOT for any specific term, contract, etc, is deemd to be at will and the employee can be discharged for any or no reason not contrary to law.
This is not to be acted on, as you have already consulted an attorney, as facts may be present untold to us, or do not seem important to you, that could create a cause of action.
HOWEVER, un unjust termination, although legal, is eligible, fact dependent on job time over the year, etc. for Unemployment benefits, as you know already.
You say you want to file with the EEOC?? On what grounds?? Race, color, sex, religion, actual sexual harassment?? You did not mention any of these??

