Home button broken; iPhone 6 won't turn on

My iPhone 6 has the most recent software available.

It randomly stopped working yesterday as I was on it. First, the screen turned black, and wouldn't turn back on when i pressed and/or held down the power button.

In addition, my home button is unfortunately broken, so i have been using Assistive Touch. Where I would usually force-restart the phone, I couldn't.

I tried charging it, and the phone is not dead. I can feel the vibration when I push the switch on the side of the phone, and when I say "Hey Siri" I can use her.

Help?!? Thank you!!!!!!