Possible Clues:

• Long to dress daughter with outstanding accessory
• Bandanna
• Cotton square
• Sneeze catcher
• Eat one's heart out over head of department and chairman with bandanna
• Piece of material taken from Desdemona (Othello)
• Piece of material used to wipe one's nose
• Snot rag
• Stuffy beak might benefit from it?
• Nose rag