iPhone 5 only boots up half way after update.

So I have an iPhone 5, and it's not even a year old. It never had any problems with charging or major glitches that would interfere with its functionality, up untill this point. I saw that there was a new iOS update available (iOS 7.0.3), and decided to install the update wirelessly(from iOS 7.0.2).
I went into settings and presses update software, and it said verifying update, then it went to the screen with the apple symbol and the bar that represents the update being installed. Like usual, the bar filled in a reasonable ammount of time and the phone began to reboot.

Problem:

The screen went dark after installing the iOS 7.0.3 update, and lit up again with the apple symbol, like you would see when turning on the device normally. I was waited a while to go back to my phone thinking that everything was in order (aproximately 1.5 hours), and upon returning I found that the phone was still booting up. I touched it to find that the entire device was really hot (I guess it had overheated itself trying to turn on), and to no avail, I tried to shut it down. The only thing my iPhone is able to do now, is run out of battery, or, when it is charging, overheat itself and display the booting up screen. I also tried pulling out the simcard and putting it back in, and pluging the phone into my computer, but because the phone is constantly attempting to turn itself on, the computer isn't able to recognize that the phone is plugged in, and the phone's state of unresponsiveness is left unaltered.

I was wondering what my best options are in terms of having a working phone: sending it in for a replacement, taking it to an apple store to get a technician's opinion, or is there anything else I could try/do?