Hi Alison Looby,
Thanks for posting here!
Because you can receive the pop-up notifications, the Outlook desktop alert was turned on, the problem is that you cannot click to open the message. This is more likely
due to a problem with the Outlook application, I suggest you create a new profile (Do not delete the previous profile), new profile will configure your account, data files and all
kind of settings again, here is the reference: https://support.office.com/en-us/article/Create-an-Outlook-profile-F544C1BA-3352-4B3B-BE0B-8D42A540459D
And
try to start Outlook in safe mode to check the issue: typing outlook /safe in the Run dialog on Windows. > In the
Choose Profiles dialog box, accept the default setting of Outlook and choose
OK. > If prompted, enter your password
and choose Accept.
In addition, it is recommended to update the Office to the latest version to see the results, if scenario persists,
we can try to repair Office from Control Panel (Please back up the data in case), here is the reference:https://support.office.com/en-US/Article/Repair-an-Office-application-7821d4b6-7c1d-4205-aa0e-a6b40c5bb88b
(select Quick Repair)
If problem still persists, please share the Outlook version to us:File
> Office Account > entire screenshot of Product Information. (remove the PII please)
We appreciate your understanding and cooperation, welcome back to us if there are any updates.
Thanks,
Linda