Welcome to the Apple Support Communities! I understand that you have upgraded to an iPhone 5c with AT&T as your carrier and when you send a text (iMessage) to another iOS user it does not send as iMessage but defaults to SMS. Furthermore, when that person responds to you, you do not receive that message either. The following article explains how to isolate and troubleshoot Messages. I suggest starting in the If you can't send and receive iMessages section and if the issue is not resolved after those steps, continue to work through the article.
If you can't send and receive 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
- Check iMessage system status for current service issues.
- Go to Settings > Messages > Send & Receive and make sure that you registered iMessage with your phone number or Apple ID and that you selected iMessage for use. If the phone number or Apple ID isn't available for use, troubleshoot iMessage registration.
- Open Safari and navigate to www.apple.com to verify data connectivity. If a data connection isn't available, troubleshoot cellular data or a Wi-Fi connection.
- iMessage over cellular data might not be available while you're on a call. Only 3G and faster GSM networks support simultaneous data and voice calls. Learn which network your phone supports. If your network doesn't support simultaneous data and voice calls, go to Settings > Wi-Fi and turn Wi-Fi on to use iMessage while you're on a call.
- Restart your device.
- Tap Settings > General > Reset > Reset Network Settings on your iPhone.
I hope this helps,