Where are my iPhone Messages notifications?
Often a hard reset of the device will fix problems. Powering off and back on doesn't do the same thing as it does for a computer - it's more akin to hibernate mode in that its drawing no power, but nothing (RAM etc) is cleared.

To do a hard reset, on iPhone 6s and below, press and hold Sleep and Home until the Apple logo appears. On iPhone 7 and higher, press and hold Volume Down and Home.