Logic around email distribution

Several of our forms have sections that are "For Internal Use" in accounting.  For example posted or billed.  I want to be able to update that field without it emailing everyone.

The only would to prevent sending all the notifications would be to set them to send conditionally:

https://www.jotform.com/help/167-How-to-Send-Email-Based-on-User-s-Answer

Add a field in your "For Internal Use" only section or use a field currently in the form to denote whether or not an edit is being made.  Only send the initial email if that field isn't filled or under some other circumstances.  That way, the initial email will send when the admin section isn't filled but will not send if it is.