Have lived in the Chicago area all my life. Several friends have had issues such as yours.
They called the Illinois Tollway system (I think you can find them online) asked for forgiveness and offer to pay the tolls. In Every case they were accommodated.
I would honestly explain that you have been traveling with a child that has issues and were not even aware that there were tolls to pay. Offer to pay telling them your financial situation.
Good luck, I hope you find them as compassionate as I expect they will be.
My only concern is that you got this big bill before you realized your error
Let all know how it works out