I was told that it's is correct to use with a noun following it, i.e. it's nose. I've always used this, but now I'm confused.
No, that is incorrect. "Its nose" is the correct form to indicate possession. "It's" is not the possessive form of "it"; rather, it stands for "it is", as in "It is nice out today". It may help if you remember that none of the personal pronouns have an apostrophe to indicate possession: "my", "your" (singular), "his", "her", "its" "our", "your" (plural), "their". PaulM