I understand what you want is having links to your social pages on top of the screen, fixed links to pages that is. What I would suggest is using the plugin feature called Custom Menus to create Toolbar items linking to whatever pages you want. You’ll need to create as many menus as icons you want, so you can style the item with the corresponding icon. I’ll describe how to add the Facebook icon and link and you may replicate with others, at your will.
First we’ll create a WP NavMenu from the WP Appearance > Menus page, call it Facebook (purely a reference here)
Then, add a custom link to that menu, with the link to the target social page. You also need to give it a name at this stage, which will show in the menu (or the Toolbar), so you’ll want to put a single space char in it to actually hide it.
Second, go to the plugin settings page > Custom Menus tab, and define a custom menu with the following elements: name, select your new menu “Facebook”, location, right of the Create menu (or anywhere else on the Toolbar), and fonticon, choose the Fb icon from the WordPress dashicon pack (code is f304). Save from the button at the bottom of the plugin settings tab, the Fb icon should appear in the Toolbar, linking to your social page.
Hope this helps