How odd - you might need to trash your preferences or reinstall After Effects - duplicating the comp shouldn’t affect the original. HOWEVER - if you have nested comps within that duplicate anything you do to them will happen to the other comps that have them. So you will need to duplicate everything.
Easiest way to do this without hunting for every single nested comp would be to select the comp in question, reduce project (this deletes everything that isn’t necessary to that comp) save-as a different file name and then open the original file again and import that reduced file into your main project. Voila! - duplicated comp and the nested comps do not reference the comps in your main timeline. I would rename them to avoid confusion later on though.