“My days of young” or “my days of youth” is correct?

No one would understand the phrase "my days of young (young what?)".  Your days of youth, though, would be very clear.

"Of" is a preposition. Prepositions are followed by nouns, not adjectives.

A feeling of happiness, NOT a feeling of happy

A touch of elegance, NOT a touch of elegant

Days of youth, NOT days of young

Of the two choices, "my days of youth", is the best.

Even though not correct, it can be used in a poem. Or some kind of prosaic writing.

"My days as a youth". This is how I would say it.

My days as a youth 

S.S., the preposition "of" requires an object, and it has to be a noun, noun substitute, or a pronoun. "Young" is an adjective, so it doesn't work.

My days of youth <-- simple noun as the object of the preposition "of"

My days of you <--pronoun as the object

My days of weeping <--gerund (noun substitute) as the object

My days of weeping over you <-- gerund phrase (noun substitute) as the object

My days of being young <--gerund phrase as the object

"Days of my youth", is the most commonly used syntax for the expression.

It's dependent on the what the rest of the sentence is, so "My days of youth" could be used too.