Are you making changes OUTSIDE of AE, like in a Photoshop file that you imported into AE? If so, then any compositions that use that Photoshop file will reflect those changes.
When you want to work in the duplicated comp, be sure to double click on it in the Project window (so that you’re not working on the original comp).
Other than that, I’m not sure why changes to Comp B would affect Comp A.