A word on your medications: if you have any prescriptions that are liquids, they're not subject to the 3-oz. limit. Run them through in a separate ziploc bag, in the original container with the prescription label.

Yes, 47 minutes is a short connection, but other than being prepared with a map of the terminal there's not a lot you can do now, except worry. I'm really good at that, too! If you wake up the day of the flight and there are storms or other conditions that could delay flights, be prepared with a list of later flights from ORD to CLE, both on your original airline and on alternates, so that if you're rebooked you know what the possibilities are before you call. You might even want to be prepared with info on hotels nearby- the airlines pretty much leave you on your own if you're stuck overnight so it helps to know what's in the area. Both DTW and ORD have hotels connected to the airport- convenient but not cheap.

As you get closer to your travel date, you can get onto the airline site and see what gate the same OMA-ORD flight landed at and what gate the ORD-CLE flight used for takeoff from ORD. No guarantee, of course, but a pattern is a good indication of the gates you're likely to use. You still need to listen to the flight crew announcement as you land at your connecting airport and keep an eye on the monitors when you get into the airport.

Probably more detail/planning than most people need, but you strike me as someone (like me) who worries about every detail and feels better with more information and a Plan B and Plan C in case things go wrong. Chances are they won't. Have a good trip!