Mate , in essence you want to date with your parents permission ? 
thats what you basically want .. because practically looking at it .. you are either going to be engaged to be able to meet your future partner with your parents permission and get to know her for a few years … OR you are asking your parents to let you meet with girls and get to know them without being engaged , which no girls parents will allow you to do..
to be engaged , your parents will find it hard to explain to any girls parents why their son is the best choice for their daughter .. all parents want settled sons in law , individuals who are ready to take on life’s fiscal responsibilities …
my son will one day become an xyz.. is too much a risk to be taken by a girl’s parents … know what i mean?
it clearly indicates that you may be ready in your mind for it , but in essence you have yet to learn alot more in maturity and give it at least until you finish your med school … otherwise even if you are engaged , and lets say after 3 years of knowing your fiancee you decide you dont like her … are you going to break off the engagement? that wont be fair to the girl… right?
so let it be for the time being … and an important thing : the way you view life , changes by 180 degrees the day you step into your practical life … your priorities change , your friends change, what you look for in a partner even that long list changes !