Battery Failure in iPhone 5?

Recently updated to 7.0.6 and for about a week my phone would turn off every 10-15 minutes unless it was on charge. This was already incredibly annoying and meant I had to bring my charger everywhere to turn it on as my lock button had broke about a year ago. I had to plug it into my car stereo, charge in it Sixth Form and have it on charge at home. On Sunday the phone went off as usual but now won't turn back on. When plugged in, it gets to the white screen with the Apple logo, turns on and repeats for hours. I've tried everything I can including the recovery mode etc, but constantly get errors from iTunes. I've lost everything trying to restore it which didn't work.

What's the best course of action? I've had the phone for about 18 months so I don't know if I'm covered by warrenty. Will Apple replace or repair it in store?