Hi,
In your case I would restart from scratch.
Remove (Sign Out) on the iPhone of the Apple ID.
Disable the app on the iPhone (It signs the Number out)
On the Mac untick the iPhone Number option.
Sign Out of the Apple ID.
Then turn the iPhone App on again and wait for the number to verify.
Add the Apple ID back to the Mac version.
Test by starting an New Message on the Mac and manually type in the iPhone Number including Country Code.
If that works make sure the Mac and iPhone are on the same LAN.
Add the Apple ID back to the iPhone for Messages.
Accept the pop up on the Mac so it has the iPhone Number again.
IF on the Same LAN then set Text Forwarding.

7:23 pm Sunday; December 10, 2017
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)