Apple ID not working on MacBook after password update

I know this has been posted before - numerous times - and I've searched or answers, and tried a bunch of things however what is surely a very simple task is not working for me (and driving me nuts).

• I had issues with my Apple ID recently where I was prompted to change my password. I had to change it several times before Apple got the process to work (long story)
• The use of my Apple ID to receive text messages on my MacBook Air I haven't been able to reinstate.
• I will get text message sent to my email - but not my phone

In System Preferences:

• I've gone to User & Groups and deleted my Apple account and readied.
• Internet accounts lists my details, but doesn't give me the option to change my password
• My phone (as a device only) is part of my account - but I think somewhere I need to list the actual phone number - can't find this.

In the Messages app:

I've deleted my Apple ID and re-added - however this doesn't prompt for my phone number anywhere

Any thoughts are much appreciated.