eMember doesn’t have any functionality to show different menu items based on the membership levels.
Shortcodes only work on Post or pages so the “emember_protected” shortcode won’t work on the sidebar.
However, if you know a bit of PHP then you should be able to put some coding to achieve what you want. I can tell you how you can get the membership level of the logged in member and then you can place “if” statement around your logic.