I had this same issue to a number I had been texting daily for months! After I tried everything--I figured it out! Even after I deleted the contact and set it all back up again, it still wouldn't work and I would get the "+1(1)216116-11 Error Invalid Number Please re-send using valid 10 digit number" error message. BY chance, as I was typing in the number for a new trial text, the number popped up from "recent history" (the list of all recent texts to that number or name). Even though I had deleted ALL texts to and from her and all contact info, the number was still stored elsewhere. It dawned on me that her number and her contact info was stored in the memory as "recent text history". I had to delete every instance of a text that had her number in it (including group texts), then when I reentered it, it worked! I believe the whole thing started when someone had her incomplete number in a group text, and from then on, it was getting her number from that recent text instead of mine! I found it by accident and there HAS to be an easier way, but here are the steps:
1. Delete the name and number from your contact
2. Start a new text by typing in the first letter or so of the person's name (or the digits of the number) and they should still pop up in a drop down box
3. Instead of selecting it for the text recipient, select the little "i" beside it and a new menu will pop up (that is the RECENT menu)
4. Select REMOVE from the top right corner
5. Do this for every instance with the name and number in it
6. Try a new text--nothing should pop up when you enter the number if everything is removed. It should now work
Hope this helps someone else!