Why do I keep receiving my own text messages when I text ONE of the five lines in our family plan?
I just figured this out as I had the same issue.

What you need to do is click on your Settings app and scroll down to the green messages icon, click on that and scroll down to the Send &amp; Receive setting. Next to this, it will have the number of addresses, that is: two addresses, click on this and untick the number and email address that are not yours. This should cure the problem for you.

If you have FaceTime active, then I’d advise checking it to make sure that only your number and your email address are filled in.