've broken my phone can take it somewhere

Hi,

well basically, i got my iphone 5 on christmas day, therefore its still under warranty, well my lock button doesnt work properly, you have to really firmly press it down on the left side of the button to get it to lock, also, i've had two people to ring me today and neither of the calls came through, my 3g doesnt work anymore and im not getting notifications when texts come through, i don't want to have to pay for it considering i've had my phone for less than 3 months, and i haven't dropped it or anything, i take great care in my phone and i rely on it for so much, that i really need it, if i took it into a large apple store with proof of purchase and warranty, would they give me a new one?

thank you