The unnamed medical school affiliated with County General features in several storylines throughout the show.
Possible identification of the school
University of Chicago
During the first several seasons of the show, helicopters serving County General are clearly marked with the colors and logo of the University of Chicago. Chicago's Pritzker School of Medicine is located in Hyde Park, a somewhat rough urban environment not dissimilar to how County General is depicted. Later in the series, characters frequently speak of the University of Chicago hospital as a place that exists in the show's universe and is distinct from County General.
In the graduation ceremony depicted in John Carter, M.D., the seal of Northwestern University is visible on the podium.
At a later graduation shown in Midnight, the Latin phrase "quacumque sunt vera" ("whatsoever things are true") is displayed on a banner hanging above the podium. This is the motto of Northwestern University.
In Masquerade, Carter wears a Northwestern sweatshirt while living and working in the medical school dormitory. As Carter previously stated that he attended the University of Pennsylvania as an undergraduate before going to med school, the most likely explanation for this attire is that the dorm he is in is operated by Northwestern. Northwestern's Feinberg School of Medicine and affiliated hospital operate in downtown Chicago rather than at the university's main campus in suburban Evanston. However, much like the University of Chicago, Northwestern's hospital is explicitly featured as a different place than County General as the series progresses, including when Corday seeks a consultation from Dr. Kotlowitz there, when Drs. Benton and Finch take new jobs there, and when Dr. Pratt attempts to move his residency there before reconsidering.
Rush Medical College
The real-life inspiration for County General, the John H. Stroger Jr. Hospital of Cook County, is affiliated with Rush Medical College. "Rush" is referred to as a different hospital than County in the episode How the Finch Stole Christmas.
The next career step after achieving full-time attending physician status at County General is receiving associate professor status at the medical school, followed by being granted tenure. John Carter achieves tenured professor status, which is denied to Susan Lewis. Mark Greene negotiates for early tenure with Donald Anspaugh but does not receive it prior to his death. Elizabeth Corday is removed from the tenure track as punishment for her unapproved transplant operation in Try Carter, though must have been an associate professor prior to being named chief of surgery. Per a remark by Kerry Weaver in Finders Keepers, all department heads at the hospital are required to be associate professors or above, indicating that Weaver and Corday achieved this status at some point offscreen. Other characters who had long careers in hospital administration such as Robert Romano likely hold tenured status.
Peter Benton and Mark Greene attended the medical school prior to season 1 of the show, during which they are residents at County General. They were in school at the same time and became friends but were not in the same graduating class; Benton is approximately three years younger than Greene.
John Carter, Abby Lockhart, Neela Rasgotra, Greg Pratt, Lucy Knight, and Jing-Mei Chen are all introduced to the series while students at the medical school. Other characters begin in the ER after being matched as interns following the completion of medical school elsewhere.
In A Walk in the Woods, Robert Romano and Peter Benton serve on an admissions committee reviewing applications to the medical school. Peter is briefly appointed to head a diversity initiative following a media backlash over low African-American representation at the medical school.