You can give your students a link to their public Learner Profile adding shortcodes in your menu.
To be able to do that you will need the Shortcode in Menus plugin.
Once installed, access the Edit Menus tab and select a menu to edit. Then add a new menu item to it.
Now you will need to configure the shortcode to add to the menu.
Click the Shortcode tab, choose a title for your menu item (for example, My Profile) and enter the User Profile Page shortcode to the description box. Please note that you'll need to use the Public Profile Link shortcode instead of the eLearnCommerce Profile shortcode.