Display went completely black

I have a 64gb iPhone 6 running on the most recent iOS and I was in the middle of snapchatting someone and my display just cut out and went black. This isn't the first time this has happened—sometimes when I'm using Snapchat the display will cut out for a second or two and I just have to restart Snapchat when the screen comes back—but this is the first time that the display didn't come back almost immediately. The phone had more than 50% battery life, and I've tried holding down the home+lock button everywhere from 10 seconds up to 60 seconds, but I still can't see anything. However, a couple minutes after I force a reboot, I can toggle the mute switch and the phone will vibrate, and it also makes the little 'ding' noise when I plug it into the charger/into my laptop, so I'm assuming it's an actual display problem. I can't access it from iTunes because it says I need to enter the passcode & the phone won't accept touch ID since the phone went through a reboot, so I can't backup or reboot or anything via iTunes. I don't know what else to try to get the phone to start working.