Translation:I have a small nose.
The Chinese phrase sounds weird to me. It sounds like it's a word for word translation of the English sentence! I would have said: Wo de bizi hen xiao! Any native Chinese speakers who can comment?
Although this sentence is not common on its own, it doesn't sound unnatural at all. You may say it along with other facial characteristics: 我有小鼻子，大眼睛。I have a small nose and big eyes.
Especially in Chinese essays, I tend yo write like that to sound less common. Might be just me though.
It is grammatically correct, but I think nobody says it except kids.
There is a song sung at kindergarten:
Correct me if I'm wrong but shouldn't this be like ＂我有小的鼻子＂? Or is it OK without 的?
Why would you permit "small" and reject "little"? In polite English the first word has a slightly negative sound, while the second has a cute sound, where one might say it in polite speech. Because of subtleties like this you need to permit more "correct" answers.
This needs to accept "I've got" as well as "I have" and "little" as well as "small".
I wrote little but got it wrong because it's supposed to be small... same thing, right?