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Resetting the network and logging out of my Apple ID is where I would have started too.
Next I recommend closing all the apps:
- Double-click the Home button.
- Swipe left or right until you have located the app you wish to close.
- Swipe the app up to close it.
From: iOS: Force an app to close
Then restart the iPhone:
iOS: Turning off and on (restarting) and resetting
If the issue persists, try toggling Airplane Mode on, then back off in Settings > Airplane Mode, then test the issue again.
If it still persists, I would follow these specific steps from the article:
iOS: Troubleshooting Messages
- See the iPhone Troubleshooting Assistant.
- Verify that every phone number in your contacts list includes an area code.
- When sending to existing contacts, ensure that your contacts include the full phone number, and not just the information needed to dial locally.
- If you have recently ported your number from another carrier, please contact your current carrier to verify that the porting process has completed successfully.
- To send and receive MMS messages on your iPhone, verify that your wireless carrier supports MMS2.
- Ensure that MMS Messaging is turned on in Settings > Messages.
- Verify that your phone is able to access cellular data.
- Some carriers allow you to edit your APN (Access Point Name), which may prevent MMS from working.
- If you are roaming outside your calling area, make sure you have Data Roaming turned on in Settings > General > Cellular to send or receive MMS content.
- While on a phone call, you will be unable to send or receive MMS messages when using an EDGE, GPRS, or any CDMA cellular data network. After the phone call ends, you will receive any incoming messages. If you tried to send an MMS message, you may need to send it again.
- If the issue persists and your wireless carrier has confirmed that your wireless account is provisioned2 for MMS, restore the iPhone.