I googled Transylvania Medical School, Louisville, KY - 1856.
Several websites came up, and the first 4 were Transylvania Medical School, Louisville, KY. From there I had to choose the approximate date of my ancestor's entry into the medical school. I found it. I also found the commencement bulletin handed out to the graduates, plus those who earned honors.
Depending on when your ancestor matriculated, the school changed its name sometime in the late 1800s from Transylvania Medical School or College to Louisville Medical College or School.
Hope this helps.