Mercutio uses puns to make fun of Nurses appearance
The whole idea of this part is that Mercutio and Benvolio are making fun of Nurse's appearance. You can tell this in the like "Good Peter to hide her face for her fan's the fairer face."
Knowing this you can eliminate the option of Mercutio complaining about his clothing.
All Nurse says in this piece is "Peter," and "My fan, Peter." She is not using puns to request her fan, she is simply asking for it. She is also not mocking Benvolio and Mercutio.
