Ipod having trouble charging..cable bent. A new cable from Apple free?

Ok so I had my iPod touch 4g for a few months now and overtime the cable got bent, like just a little beneath the white part that goes into the iPod. Because my cable is bent I'm having trouble charging it and if I adjust the bent cable a certain way it will charge but sometimes it won't and it gets really annoying. Sometimes a little message comes up "charging is not supported with this accessory" but once I adjust the cable a certain way and my iPod charges it goes away. Anyways, my main question is will I be able to get a new cable from apple for free? If so do I need to go to the Apple store in person or can I like call them and they will send me one for free? My mom blames the problem on me because I took the cable out of my ipod too fast like I'd pull it and stuff so I will have to pay for a new one. I'd love it to be free.