Hey there, let me ask you a few more questions, so I can get an idea of how you're sending your messages. What version of iPhone do you have? Are you getting an error message with a number, or code? Are you connected to WIFI? How many bars do you have for signal?
I need to speak to someone so that I can further explain it does matter who I am send a message to or who is sending a message to me I can not get messages if I am on a call. If these is an emergency and I am on a call I will not know until I am off the call and the is hazardous I have kid and they love to text this is ridiculous.
My apologies, I was under the impression you were having issues sending and receiving text messages all together. The issue that you are experiencing is that we are currently testing it in some areas for Voice Over LTE (VoLTE). Very soon, you will be able to experience this great feature. Unfortunately until the towers are all upgraded, there is nothing we can do unless, you are connected to WIFI. You can receive the messages then while on a call.
Android users can utilize Calling Plus so they can talk and surf at the same time. Once we get VoLTE up and running everyone will be able to talk and surf. This is very exciting news. Hang tight and we will get there together.