Someone else may have a better suggestion, but first of all, Access won't just tell you when something new has happened. You'll need to ask it if something new has happened.
Having said that, I would suggest maybe using a hidden form with a timer event to refresh the database at a specified interval and then if the records in a table you are using for the messages has changed then have code to trigger a pop up message box.
If you have your app minimized you can still open a dialog in Pop Up mode and it will come on screen. However, it will not automatically jump to the front. So, you'll need to program for that.
Hope that helps.
Smoke me a kipper, I'll be back for breakfast
BL