By definition, Dartmouth is an Ivy League school.
Also, Dartmouth > UNC
With an acceptance rate of 6.6% I would hardly call Ohio State Medical School “average” (post #4), OP. It’s ranked in the top quarter in research among US med schools.
It’s interesting how thirty years of USNews indoctrination has reduced the perception of the Ivy League to a conglomerate of the best research universities in the country. When the term, ivy, first began to be tossed around in the 1930s I can assure you it nothing to do with the strength of a university’s graduate schools; Brown probably had just as few as Dartmouth did. As others have pointed out, it grew out of the intercollegiate athletic movement of the early 20th century which was almost entirely run by undergraduates. It resulted in eventual round-robin play between seven of the oldest colleges in the country (the term “ivy” was meant to evoke images of that invasive, non-native species climbing up ancient walls) plus Cornell which was a football powerhouse at the time.
Your acceptance to Duke only means that you would have been a viable candidate in the Dartmouth pool, it does not mean that you would have been accepted. While you were accepted to Duke, you actually attend UNC-CH. Hopefully you are happy there and the school meets all of your needs.
Since the question has been asked and answered, and this thread is going circular and has outlived its usefulness, it is now closing.