Iphone 5 bought in the US, could I replace it?

Iphone purchased in Feb. 2013. The phone is not at all damaged on the outside. But problems occurred during an upgrade (as notified on the phone) and now I can't turn it on. Only the white apple symbol remains on screen.
I have the case it came with and my receipt. Could I ask for a replacement in any apple store in US?
Would I have to pay extra?

If you have a warranty you could be if not you will have to pay.