Dropped Iphone 5 issues

I dropped my iphone 5 on the sidewalk yesterday. It was in a hard case, and there appeared to be no exterior damage. For the rest of the day, it would connect to Wifi but not the verizon service, however, the battery depleted very quickly. I plugged it into its charger and it slowly began to charge (much slower than usual), however, it became extremely hot while doing so. After a few hours, it was only 50% charged and was burning hot, so i unplugged it from the charger.

However, when I plugged the phone into its charger today, it wouldn't start! It flashes the white apple screen and then goes back to a black screen when it is plugged in to either my computer or the wall for charging.

Is there anything I can do to fix this? Should I take it to the Genius Bar? Would an issue like this be covered by warranty?

I've had the phone for less than a year, if that makes any difference.