after upgrading to Windows 10, I had issues with the Windows App Store so at Microsoft's suggestion (at windowsphone.com) i "refreshed" my phone and lost many "Lumia" specific apps (which I'm not too concerned about) but also lost the ability for my phone to send and receive SMS text messages. How can I get this back or is there a fix or a replacement app or what?
When you say "refreshed" did you do a hard reset after upgrading to Windows 10 Mobile? If not try that first.
Lastly what phone did you have?
Worse comes to worse roll back to Windows Phone 8.1, FAQ - How can I recover/reset/restore my phone software? - Microsoft - USA
I have a Lumia 735 (came out in may IIRC bought by me in August) so it's fairly new. By refreshed, yes, I mean I did a hard reset.
It could be a defect in the latest build with the 735s. You can try rolling back to 8.1, test SMS and if that's fine try upgrading to Windows 10 Mobile.