Q: Why won't my message or phone notifications ring or vibrate when my phone is locked.

Did you already check the settings for your notifications?

Use Notifications on your iPhone, iPad, and iPod touch - Apple Support

If this worked before the update to 9.3.1, did you already try to force restart the phone by holding the sleep and home button for about 10sec, until the Appel logo comes back again? You will not lose data by force restarting the phone, but it can cure some glitches after installing new software or apps.