It was not made clear on the show if Starfleet Academy had a College of Medicine. Her rank of Lt. Commander suggests that she was an Academy graduate and "Imzadi" by Peter David has her attending classes at the University on Betazed. DS9 suggested that Dr. McCoy (also a Lt. Commander) got his degree from Ole Miss. Therefore, it seems that medical professionals complete their Medical degree at a "civilian" university before entering the Academy. Sorry, I don't think there is an answer to this question in "Cannon" so we'll just have to speculate.
I checked, and it is canon that Deanna Troi is a Starfleet Academy graduate, entering in 2355 and graduating in 2359. She is a Lieutenant Commander. This I think is from the crew manifest readout in ST:TNG "Conundrum". I've heard the story that McCoy went to Ole Miss--that McCoy did not attend the Academy comports with the fact that he did not know what "dunsel" meant in the Star Trek: The Original Series episode "The Ultimate Computer" (Spock explains to him that this is a term used by midshipmen to refer to "a part which serves no useful purpose").
Of course, we know from the 2009 reboot movie that McCoy did attend the Academy (an instance of canon possibly contradicting itself, at least by implication, although it is possible McCoy did attend the Academy even by ST:TOS canon, he simply had never heard the term "dunsel" before). Troi's Psychology degree from the University of Betazed may therefore be a graduate degree of sorts. She has described herself as a "practicing psychologist" (ST:TNG "Haven"). It certainly is possible that the Academy has no medical school; however, there must at least be accredited non-Academy medical programs that teach xenomedicine courses that qualify physicians to practice space medicine in Starfleet ProfessorTrek 01:30, July 19, 2011 (UTC)
Troi is an Academy graduate, otherwise she wouldn't hold the rank of Lt. Commander. A person has to attend the Academy for 4 years or so to become an officer. It is uncertain as to weather she had taken psychology or other medical sciences courses while in attendance there. TrekFan1984 Ends (talk) 00:54, August 11, 2014 (UTC)
Just because she held the rank of LCDR doesn't mean she attended the academy. It would be extremely inefficient for every officer in an organization the size of starfleet to attend the academy. It's likely they have some form of ROTC program. Given the Ole Miss reference and his lack of knowledge in academy lingo, it's likely that the prime universe McCoy was a ninety-day wonder (or futuristic equvalent thereof), even if his alternate universe counterpart was not.-Cpthunt (talk) 03:56, August 14, 2014 (UTC)