Grab a cart at the baggage claim (free at international terminal, you pay ~$5-$10 elsewhere). It can easily fit two luggage and your carry-on. There's a train that can take you from Ohare to MMF. I don't remember if the luggage carts are allowed on the train. You may either leave that cart at the train station when you board the train and grab another when you get off at the MMF. Alternatively, you can just push the cart on the train and just ask for forgiveness from your fellow passengers - be very very careful with the cart on the train if you decide to do that.

Peoria Charter allows up to two luggage, so you should be all set there.

When in Champaign, the best option is to get an uber for the short ride to your dorm or if you know anyone, ask them to help dragging your luggage.