I have a sweater that was stained so I ordered another of the exact same sweater from the store to be delivered to my house. If the sweater arrives during the 9 days, it permissible to wear the sweater?
The new sweater should not be worn in the Nine Days.
New or freshly laundered clothing are not worn in the Nine Days, provided the garment is significant (not underwear etc.). A sweater is (usually) a significant garment, and therefore must not be worn when new. However, you can wear it first on Shabbos, and after this it can be worn for the rest of the Nine Days.