It won't turn on:(

I recently got a new phone on my birthday. I shut it down and left it for about 30 minutes, when I came back i plugged it in, it showed the battery charging thing, I held down the power button to turn it on, it just turned the screen off. (Note it said it was at 41%) I unplugged it and held the power button down. It didn't turn on, I plugged it back in and the little L.E.D on the top of the screen was flashing red. I unplugged it and it stopped, now whenever i plug it in it flashes red. Please help!