It seems like you’re getting a warranty and insurance mixed up here. They’re not the same thing.
Warranty: Covers you from defects caused by manufacture. If your iPod unexpectedly stops working, Apple will repair or replace it for you. They do this for free because it’s their fault.
Insurance: Insurance will protect you from accidental damage, theft, loss, or other unfortunate outcomes. Apple don’t provide insurance. You need an insurance company here.
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It is possible that your iPod touch is covered by your home contents insurance, if you have this type of cover. You may have to pay a small amount, but the insurance company will handle the repair or replacement.
Your other option is to take it to Apple for a repair. They can give you a quote for replacing the screen.