My iPhone won't turn off

If it won't let you force restart (that's very strange), I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.

Settings>General>Shut Down (the last option at the very bottom).

Or, if you can't go to that option, try a "forced" restart of your iPhone using these instructions:--> Force restart iPhone – Apple Support

Regards

Giulio