Can I file suit against my employer if I am an Illinois resident and my employer is in Ohio?

First, I think you are asking if you can file suit in Illinois. That is a question of venue and jurisdiction. If your employer does business in a county in this state, then you can file in that county for venue purposes. If the suit arises from your employment contract to be performed in this state by a state resident, then you can sue on the contract in this state/county. Jurisdiction and venue are fact-specific, and you'd need to provide more facts to an attorney to say for sure on the best place to file suit.

Second, it is VERY difficult to overturn an arbitrator's decision. Typically, there must be fraud, bribery, or a totally egregious, wanton error to overturn the arbitrator's award. As for the findings of fact, they are almost never overturned. You have better chances with the legal findings, if they are so erroneous as to make the decision totally unreasonable. But this is a rarely won battle, indeed rarely fought because of the likelihood of success.

You should definitely contact a lawyer about the case. I hope you had one for the arbitration and you should talk to him/her about this situation. If you are not comfortable with him/her, either get yourself to a place of comfort or find someone you are comfortable with.