Dilemma
From 'Vocabulary' part of The ABC Of Plain Words by Sir E Gowers (1951)

This is a word of precise meaning, and should not be abused. It ought not to be treated as the equivalent of a difficulty, or, colloquially, of a fix or a jam. To be in a dilemma (or, if you want to show your learning, to be on the horns of a dilemma) is to be faced with two (and only two) alternative courses of action, each of which is likely to have awkward results.