screen black and unresponsive but I can hear notifications

I got this iPhone 6 from the AT&T store a little over a month ago and I keep it in a lifeproof case. I haven't had any problems with it previously but while using it today, it just went black. I assumed it was dead so I plugged it in and nothing happened. I then took the case off and realized my phone was really hot. I let it be for a while to cool down. I can still hear notifications but the phone is unresponsive to the lock and home button. I tried to do a hard reboot by holding the home and lock buttons for 10 seconds but it didn't work. Any ideas on what's wrong or how to fix it would be infinitely appreciated.