A plea of guilty can be used against you in a civil lawsuit. Essentially, the person suing you would not have to prove that you violated your duty of care to the other driver -- the guilty plea would be pretty much all they would need to show.
If you feel you entered your guilty plea under circumstances where you did not understand your rights, your attorney should file a motion to have the original judge overturn the verdict and ask for a trial or a no contest plea. If more than 30 days have gone by since the verdict, this is hard to do under Ohio law, but it is possible if a "manifest injustice" occurred.
Ohio Crim.R. 32.1 governs motions to withdraw guilty or no contest pleas and provides that “[a] motion to withdraw a plea of guilty or no contest may be made only before sentence is imposed; but to correct manifest injustice the court after sentence may set aside the judgment of conviction and permit the defendant to withdraw his or her plea.”
See also the Supreme Court case State v. Xie (1992), 62 Ohio St.3d 521
You will likely get a better result with an attorney who regularly practices in the court of the judge who convicted you. Good luck.