Hey Lindseyb0813,
Thanks for using Apple Support Communities! I understand Message notifications from your Mac aren't working as expected. I definitely want to make sure all your features are working as expected, and I'm happy to help.
If you haven't done so already, lets restart your Mac and check if the same behavior continues. Use the steps for restarting here: How to turn your Mac on or off
I would also recommend testing if this behavior continues in Safe Mode as well. You can find the steps for that here: Use Safe mode to isolate issues with your Mac
If this behavior doesn't happen in safe mode, restart your Mac and login as normal. Then, let us know if the behavior returns.
Thanks again, and have a great day!