Once you publish to Tableau Server, it's not your personal account who's accessing the shared drive, it's the account that Tableau Server is running under (Run As User):
The majority of times I see a problem like this it/ss related to permissions missing in that shared drive for the run as account. If you compare the permissions granted in those folders, do you see accounts on the shared drive that works that are missing on the one that doesn't? Alternatively you could check with your Tableau Server administrator what is the Run As User and then add permissions for that account on the shared drive.
Hope this helps!