Never fly in to O’hare if you can get a flight to Midway. O’hare flights are late quite frequently. I would rent a car to keep the cello at a warmer temperature instead of risking cracks.
Between Ann Arbor and Chicago : both the Megabus and Amtrak - both leaving from /near union station and close to the UM campus are good ways to go. Amtrak is late at least 50% of the time, often by several hours. Megabus is faster and the wifi works on it. You will have to check with them on their cello policies, but you definitely don’t want it in the unheated luggage area unless you have a carbon fiber one. . I prefer driving for two if you can get a reasonable one way rental which you can return at the airport. Hertz with AAA discount sometimes has good one way deals. The only stretch that is bad is usually lake effect snow on I-80 in Indiana and I-94 in western Michigan. On bad days it can stretch from Gary to Kalamazoo, but so far this has been a very mild winter with little snow.