「あはははは、こんなもの慣れよ慣れ。ほら、じっとしてな、払ってあげるから」
「い、いーですって、先生、自分でしますから」
「いっちょまえに照れちゃってもー。いーからいーから、自分じゃわかんないでしょ。ほら、頭の上とか」
I don't quite understand how 一丁前に modifies 照れちゃっても in this context. I understand that 一丁前に has the ideas of becoming an adult associated with it, but how does that come into play in this context? (She threw a snowball at him, and he hates the cold.)
She's teasing him. 一丁前に照れちゃって is something like "So you are no longer a kid, you know how to be shy!" (like an adolescent boy, in a situation like this where a woman touches a man)
もー at the end is もう, which is not a conjunction but an interjection like "gee", "whew". From a dictionary:
５ 自分の判断・感情などを強める気持ちを表す語。感動詞的にも用いる。まさに。なんとも。「これは―疑う余地のない事実だ」「嫌になっちゃうなあ、―」
As you can see in the example above, もー like this is usually (but not always) preceded by a comma.
