My iPhone 5s died and won't charge! Help?

I had my relatively new iPhone 5s attached to my laptop and charging, with the flashlight on. The computer kept telling me that the phone was taking up too much power and kept stopping the charging process. I fell asleep and when I woke up, my phone had run out of battery (presumably while the flashlight was on).
For some reason, I can't charge it now. When I connect it to my computer, I get the same notification that the phone is using too much power, even when my computer is connected to a wall charger itself.
When I charge the phone directly from a wall outlet, it doesn't charge. Instead it displays the attached image, with the red part flashing.
I don't know why the phone isn't charging. Have I broken it by accidentally leaving the flashlight on for too long? Please help me out here. Thanks in advance!

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