iphone upgrade, Not able to send and receive text message without data turned on

Actually your phone is sending messages as iMessage. So like many user it may face issue "Can't send/receive texts without data turned on"

Try below tips:

1. you need to change it to normal text.
Immediately after you send the message, tap and hold the blue bubble. You will get a pop-up option to send the iMessage as a text. 

2.Have you tried going into settings -> messages;  and turning on the "send as SMS" toggle

3. Turn off iMessage, go back and try again by resending the message.
once that's done, go back in to settings and turn on iMessage.
try to send another message, that should Solve the problem. You will have to do this in every text that can not be delivered.

Or you may try this:
4. Settings > Messages > iMessage > OFF, Send as SMS > ON, MMS messaging > OF