Use the Access Control pane to remove public access from whatever you are worried about. If you go to your public folder in the data browser, then select the sharing control pane by hovering at the top of the pane so the pane icons appear and then click on the rainbow icon. You should see the access control list including yourself at the top as the owner, and public (a globe icon) at the bottom as readers - in green. Delete the globe icon line by hovering at the right side, clicking on the read minus sign, and then confirming you want to remove the public. (If you need to drag it back, there is a globe icon at the bottom you can always grab to drop into the access control list.) Sorry not better documented!