Hey there Marbarc,
It sounds like you have setup Text Message Forwarding but its not working between your iPad and your iPhone. I would quit all the running apps on both devices first:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
That should get it going again. Thank you for using Apple Support Communities.