Hi,
There is a long term issue with Messages and the iMessages account that has been present since version 7.0.1 at the OS X 10.8.2 update.
This is when Apple started using the Serial Number to make the login Device Specific.
AT that time most people with issues had missing Serial Number where it had not been "flashed" back to repaired (replaced) Logic/Mother boards.
There were 2 version 8s of Messages.
These continue until we get to version 11 in High Sierra (MacOS 10.13.x)
At each update and Upgrade a few (and the number is small compared to the numbers using any particular Mac OS) who seem to have this issue.
People notice that iMessages are not syncing properly but as most use both iPhone number and Apple IDs as contact IDs the issue can be hidden.
Testing is the only way to check.
It was this phrase that made me think you were using SMS as well as iMessage
... when I use iMessage on my MacBook, texting to iPhone users. ...
If the Mac is not logged into the iMessages server it may still send SMS if linked to the iPhone to do so.
Obviously in some cases the phone might not be able to send SMS and convert it to iMessages instead.
If testing proves it is the account is not logged in then you are most likely going to need Users Tip
When the iMessages account will not Login
The last bit in that Users Tip is about phoning Apple Support (Apple Care)
Apple ID issues are free to fix. However you need to move up the chain of responders until you get someone who can check the server.
They should be able to tell you if the server is blocking your Apple ID when used by your Mac (It is Device Specific).
More recently the responders have been asking for data grabs and other log details in an effort to find out why it happens. (I have not spotted a trend for OS Version or Mac Model or particular ID types such as @me.com or @mac.com or even @icloud.com or non Apple issued emails as Apple ID)
It is no good doing a Reinstall if suggested until you know if the server is blocking the ID as if it is it will still be blocked after the Reinstall.

8:48 pm Wednesday; January 17, 2018
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)