I am being restricted from setting up new media bins for some reason. When I right click on the all media icon, I am not allowed to create a new bin. Any suggestions?
The "All Media" icon is a dedicated one that holds all media you have in your project. You can create YOUR bins by right-clicking on the Media Bins icon (which looks like a folder) and adding bins there.
Then, open the All Media icon -- so the files appear in the right-hand pane -- and drag media from there into the bins you set up. Dragging them never takes them away from the "All Media" group.