It sounds like you can send SMS/MMS messages but not iMessages. I recommend these troubleshooting steps from the article named:
iOS: Troubleshooting Messages
Issues with sending and receiving iMessages
You will need these to send and receive iMessages:
- An iPhone, iPad, or iPod touch.
- iOS 5.0 or later.
- A cellular data connection or a Wi-Fi connection.
- A phone number or Apple ID registered with iMessage in Settings > Messages.
To resolve issues with sending and receiving iMessages, follow these steps first
- Check iMessage system status for current service issues.
- Go to Settings > Messages > Send & Receive and make sure that you have registered iMessage with your phone number or Apple ID and that you have selected iMessage for use. Learn more about troubleshooting iMessage registration if the phone number or Apple ID isn't available for use.
- Open Safari and navigate to www.apple.com to verify data connectivity. Learn more about troubleshootingcellular data or a Wi-Fi connection if a data connection isn't available.
- iMessage over cellular data might not be available while on a call. Only 3G and faster GSM networks support simultaneous data and voice calls. Learn more about which network your phone supports. Go to Settings > Wi-Fi and turn Wi-Fi on to use iMessage while on a call if your network doesn't support simultaneous data and voice calls.
- Restart your device.
- Tap Settings > General > Reset > Reset Network Settings on your iPhone.
If you are still unable to send or receive an iMessage, follow these steps
- Make sure that the contact trying to message you isn't blocked in Settings > Messages > Blocked.
- Verify that the contact you are attempting to send a message to is registered with iMessage.
- If the issue occurs with a specific contact or contacts, back up or forward important messages and delete your current messaging threads with the contact. Create a new message to the contact and try again.
- If the issue occurs with a specific contact or contacts, delete and re-create the contact in the Contacts application. Create a new message to the newly created contact and try again.
- Back up and restore your device as new.
Thank you for using Apple Support Communities.
All the very best,
I hope that is not apple's reply...
So...we forgot to patch a security hole in our OS, here is a patch; BTW you may have to back up your phone and reload it as a new phone cause our patch nuked your networking protocols.
Now that I have got that out... messages are sending but seeing "message not delivered" notice. All methods besides a phone reload have been attempted.