You might want to check with your cellular provider to make sure that you have hotspot enabled and you have not gone over your allotted amount of GB for the month.
There is a known issue with some devices that have unexpected shut downs. Just check your serial number to see if your phone is affected.
If your phone is not affected, then check here If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support to see if maybe one of these steps can fix the problem.
Hope that helps!