from > http://www.gottabemobile.com/2016/01/19/ios-9-problems-fixes/
We’re also seeing problems with iMessage after the iOS 9.3.1 update. These are extremely common and we will almost certainly see iMessage problems continue well into iOS 9’s lifespan.
If you’re seeing problems with Messages, the first thing you’ll want to do is toggle the feature off and on again.
Go into your Settings > Messages > Toggle iMessage off then back on. This fix has worked for us in the past and it’s the first thing you’ll want to try out.
If that quick fix doesn’t work, reboot your device.
And if a reboot doesn’t work, head into your settings and reset Network Settings. Head into Settings > General > Reset > Reset Network Settings. This will cause your device to forget your connections so make sure you have your Wi-Fi passwords handy.
I read in another article that iMessage and Facetime CAN take up to 24 hours to "activate"