Hi jh100,
Thank you for using Apple Support Communities. I understand you are having difficulties with iMessage in macOS Mojave. I'd be happy to assist.
Before we continue further do you have a backup? If not that's alright. It's always recommended to have a backup before troubleshooting potential issues. If you'd like to make a backup here is a great resource: Back up your Mac with Time Machine
After you have performed a back up the first step I would recommend is signing out and back in to iMessage on your Mac. Here is a resource that goes over iMessage preferences and how to sign out: Change iMessage preferences in Messages on Mac
If your issue is still persisting your next step would be to further isolate your issue within a test account. Here is a great resource on using a test account to troubleshoot an issue: How to test an issue in another user account on your Mac
Enjoy your day.