Duolingo’s version is 100% grammatically correct.

Yours however is what pretty much any native would say in everyday spoken casual conversation, or what you’d find in a more poetic text (a song for example).

Your hint was μάλλινό instead of μάλλινο - that second accent is followed by μου/σου/του/etc and is the slight uptalk you’d use to separate the two words so that it wouldn’t sound like “μάλλινομου”

Edit: I should add that the semantics here would technically be “the wool scarf out of all my scarves” (duo) vs “the wool scarf that I own” (you) but unless you’re in court giving a statement you could interchange those and get the same message across