The idiom is to 'pay through THE nose', not 'my nose'. For example, 'I managed to get my car fixed on New Year's Eve, but I had to pay through the nose for it.'
As the other people have explained, it means to pay an excessive amount for something. But it's very important to get the wording of idioms exactly right. If you get just one small word wrong - even an article - the idiom doesn't work.