There were medical schools in the 19th century. A great uncle and a great great uncle were both UVA graduates in medicine. "Doctors in Gray" by HH Cunningham mentions several medical colleges. My eighteenth century doctor is a problem though. He is listed on land grants etc. as "Dr." by 1704. it has been suggested that he went to England for training as his father's biography talks of going back and forth to England several times. Maybe his son did the same.
I have an 19th century physician ancestor who was a homeopath in Georgetown.