Unless you bought a protection plan on the iPod, almost definitely not. (I work at Best Buy)
However, I would guess that the iPod does have a one year warranty on it. I would check to see what the warranty covers and take it into your local Apple store if it is covered.
However, there may be a way to get around the system at Best Buy if what happened to your screen isn’t covered in the warranty. First off, @geeky_mama is incorrect- Best Buy Geek Squad can and will fix the screen on your iPod, or they will replace it completely if they are unable to fix the iPod. However, my guess is that this would cost a significant amount of money if you don’t have a protection plan. If you still have your receipt, you can bring it in and get the cheapest, shortest plan they offer within 30 days of the purchase. You can bring your iPod in a couple of days later and they will fix or replace the iPod under the plan. It won’t be completely free of charge, but it might be more cost-effective than the other options if it’s not covered under your warranty. Good luck, and I hope this helped!