What iPod model do you have? What iOS level are you running? (See Settings -> General -> About) It should be possible to fix the slowness.
Regarding your question: No, you can't just send it in for a new one.
Some general debugging steps:
Restart iPod: Press and hold the Sleep/Wake button until the red slider appears. Slide your finger across the slider to turn off iPod. To turn iPod back on, press and hold the Sleep/Wake until the Apple logo appears.
Reset iPod: Press and hold the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears. Ignore the "Slide to power off".
Restore iPod: Connect to iTunes on a PC/Mac and do a restore.