I literally ran into the same issue myself yesterday! The fix, thankfully, is simple. Grab both devices and go to Settings > Messages and turn off Messages, then do the same for FaceTime. Then go back and turn on both FaceTime and iMessage on both devices. When turning FaceTime and iMessage back on, I'd start with your iPhone and make sure you tap "Use my Apple ID for FaceTime/iMessage" which will enable you to use the phone number on your iPad as well.
If messages still aren't syncing an hour after doing that, go back and turn off FaceTime and iMessage again on both devices, then restart the devices (hold the Sleep/Wake button, slide the slider, wait for the device to turn off, then hold the Sleep/Wake button until you see the Apple logo). Wait 15 minutes, and then turn on FaceTime and iMessage once more on both devices and it should work for you!