I think all languages have rules about using subject and object pronouns when appropriate. There is actually nothing wrong with 'you and me' if you are using them as object pronouns. For example, 'He was talking to you and me' is correct ('He was talking to you and I' would not be, any more than 'He was talking to I' would be). It isn't correct to use it when they are subject pronouns, for example 'You and me need to talk' is grammatically incorrect, although often used informally; it should be 'You and I need to talk.' As for the word order, I think not saying 'me and you' is more of a manners thing than a grammar thing. Anyway, yes, Italian also has subject pronouns (to be used when the pronoun represents the person doing the action) and object pronouns (to be used when the pronoun represents the person having the action done to them). However, Italian has both direct and indirect object pronouns, so which you use depends on whether the verb is transitive (doesn't need a preposition, like 'to' or 'on' to link it to the object) or intransitive (does need a preposition).
I'm not sure what any of this has to do with shoes though.