The University of Cincinnati was one of the first medicals schools in the USA. People from Richmond, Indiana, would not have found it unreasonable to travel and board in Cincinnati to go to the OHIO MEDICAL COLLEGE. This fore runner of UC Medicine is the foundation of the hugh complex it has become.
If you look for railroads that existed from near where the ancestor lived, you usually can find where they went if they had any money at all.
The city of Cincinnati is in southwest Ohio in Hamilton county. The UC digital library is open to the public on-line where you might find his name if he was in town attending medical school. I know they have births and deaths for the city for the 1800s. The death certificates have the doctor's names also. Surely they have a data base of of OHIO MEDICAL COLLEGE graduated.