IPhone experts: Is it my lead or battery that's causing this problem?

Hi so I have an iPhone 5C, and I damaged the lead of the charger about 3 months ago. Like the white bit on the outside started to wear away and its got worse and worse. For the best part of a month my battery lifee has seriously reduced, either it doesn't last at high charge percentages or (and this is happening very frequently) it "dies" before even reaching 0%. When charging it sometimes takes a few attempts to the phone to begin charging. Just now its not picking up the charge at all. I've ordered a new lead in case that helps but I just thought I'd see if anyone could tell me if its the damaged lead or something with the battery itself that's causing this problems? I've had a look on the Apple queries page and none of the problems seem to match mine, so I just wondered if anyone here would be able to help.

Take it to the Apple store for good advice.

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