Screen is unresponsive, can't get into any apps, can't manually turn off the phone

I've never experienced this before with my past iPhones before but mine started lagging and not allowing me to click on the apps I want to go to after my friend and I's attempt on facetiming each other. So it all started when I tried to facetime her when I was at a place that had bad reception and it would respond only with a plain gray screen even though I could tell that she was trying to facetime me but I couldn't respond to the call. It went away after a little bit and I was able to use my apps again but then I had to call my friend again and it just completely froze again, now I can only turn the flash, wifi, data and airplane mode on and off but other than that there's no response to the rest of the apps. I also tried turning my phone off by holding down on the power and volume up buttons but it's also unresponsive, it doesn't work. I can't force it to refresh because the power button just doesn't work at all. Is there anyone experiencing the same problem as I am and how do I fix this?