With certain nouns that began with an “n,” English speakers found it easier to pronounce the “n” with the article, rather than with the noun. While this was the origin of “an,” the practice spread to words that had no “n” at their start, but had an open vowel sound. That’s why many people say “an hour,” for example.

So the rule for when to use “a” versus “an” is not determined simply by whether a word begins with a vowel, but by whether it feels more natural to use one or the other.

So one says “a unicorn” or “a eunuch” because the hard “u” sound is more naturally preceded by “a’ than by “an.” You are essentially correct when you say that “an unicorn” simply “doesn’t sound right.”

It’s a process paralleled today in the phrase “a whole nother.” There’s really no such word as “nother,” but the contraction “another” (an+other) is being treated as if it were “a nother,” leaving a space (a hole you might say) for the word “whole.”

It’s what keeps the language interesting.

So in unicorn it’s the long vowel so you would say A, whereas with Umbrella, it’s a short vowel so you use AN