No need ta be so formal. Yer makin’ my neck itchy. Talk normal, got it? (Source)
I have no idea what does "Yer makin’ my neck itchy." mean. I guess the phrase has some figurative meaning.
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I think it simply means, "You're making me feel uncomfortable."
It's not an established idiom, though; I'd guess it's a creative expression coined by the author. I could only find two instances of it on the Internet (the original story, and this ELL question). Moreover, when I tried to use a more formal form ("you're making my neck itchy"), Google said:
No results found for "you're making my neck itchy".