If my case goes to trial, will the jury know how much insurance the other driver has?

No.  Not only will the jury not know the amount of the wrongdoer's insurance limits, the jury will not even be told whether the wrongdoer has insurance covering the accident.   In fact, the law forbids the introduction of any evidence that the defendant had insurance. Under Ohio law, the jury is to decide fault and money damages solely on the evidence presented.  Whether a person has insurance is not relevant to those questions.