MS Outlook auto update conflicts

I have written a VBA function that that is launched whenever a new email arrives in any one of about 6 email accounts and it does some processing, including allocating it to a folder, marking it as read and updating some records in a MS Access database. We use MS Exchange email accounts on MS Outlook and many of us share multiple email addresses but the VBA is only loaded onto my computer.

The concern I have is that if my computer is turned off for any reason, say on a day that I am not there, the processing won't happen, If I load the same VBA on all the computers then they will all be working on the same email as it arrives on each of them. Is there any recommended approach to manage conflicts. I don't really want every computer, for example, to launch the function to update the MS Access database.