iPhone 5S vibrating constantly when I view a message
There are a few more things that you can try to perform.


You can try to restart the device by holding both the home/sleep and the wake button for a few second until the Apple logo appears on the screen. And the phone restart.
Another option is to perform the restore of the phone. You need only to perform a backup using iTunes and then restore the iPhone from the last backup available on iTunes.


If these two options doesn't resolve your problem. You can ask assistance in a Apple Store center because clearly this is a problem the shouldn't occur.