It sounds like your iPhone doesn't want to power on or is stuck on a black screen since you updated to iOS 11.1.1. This is certainly not expected behavior after an update and I want to do what I can to help get your phone back on. Check out the link below for some tips that can help resolve your issue.
If your iPhone, iPad, or iPod touch won‘t turn on or is frozen
If this does not help, please let me know.