What preposition do you use with 'dilemma'?

I want to say that at some point in my life, I had to choose between two majors for undergraduate studies. Is this sentence grammatically correct?

I was in the dilemma of choosing between y engineering and z engineering to study as an undergraduate student.

Or should I say

I was in the dilemma of choosing between y engineering and z engineering on which major to study as an undergraduate student.