Just in case anyone finds this thread in 2020 or beyond and is looking for a solution. I was having a similar issue, where every time I received a text message, I would receive a 2nd notification from a really old text. I couldn't find that old text anywhere in my default SMS app.
For me, the issue was Verizon's Integrated Messaging service. I used the Verizon Messages app for a couple years, and it's been storing my texts ever since. Apparently time has not been kind to the older texts, and they are doing weird stuff with Ford Sync, showing up as unread multiple times.
Anyway, what worked for me was to re-download Verizon Messages on my phone, and scroll through the conversation of the person whose ancient text would show up. Eventually it loaded in all the texts it had saved over the course of years, including the offending text, one from 2016. I deleted it, as well as a few other problem texts, and that seemed to do the trick.
If you don't care about that text history, you can just delete your Integrated Messaging account (blows up all the texts, but doesn't affect your Verizon account). If you do want the text history, try to isolate the actual content of the text message when it shows up on Sync, go find that message, and delete it.
This worked for me, hope it works for you!