at medschool you were probably taught to pronounce it as ee because that's the Greek pronunciation and most medical terms have Greek origins. The pronunciation of ae as "eye" is the classical Latin pronunciation. The classical pronunciation tries to copy how the Romans would have spoken during the time of people like Cicero, Julius Caesar and Augustus.
As well as having the classical pronunciation, Latin also has an ecclesiastical pronunciation which is how Latin has been pronounced in the Catholic Church for the past few hundred years. This pronunciation is closer to modern Italian, pronouncing c as "ch" and ae as "ay"
Well, I must have represented the sound wrong because we weren't taught to pronounce "ae" as "ee" (the sound [i]) but rather as the sound [ɛ] (as if there was no diphthong at all and the word was written as "olive", for example).
So that's even a third variant of pronunciation ([ai], [i] and [e]) that was either made up by our department or was used at some point in the past.
It would be interesting to know how the pronunciation changed over time but I guess that is some advanced level stuff
Both of these versions of pronunciation are correct. In classical Latin we say [ei] and in traditional Latin we say [e]. This traditional way of pronunciation of "ae" comes from last years of Roman Empire. Peasants used this way of speaking. Then this version of reading "ae" moved to medieval Latin, and now we have it in traditional Latin. So, there are some differences between classical and traditional Latin. Moreover, different national schools have their owen version of Latin pronunciation. For instance, you can compare pronunciation of "ci" from famous phrase "veni, vedi vici" in Italian and Ukrainian schools of traditional Latin. Both of them don't sound like classic Latin ( "vitsi" [віци] and "vichi" [вічі] respectively). And we can say that all of them are correct because thousands of people have been using them for centuries.