Is there a module that helps link similar articles together and insert them into each other? I'm looking for the module that would allow me to manually link related articles together and to then set them to appear within the body of content - as links.

What would be your recommendation?

I tried to find different modules, but I need specifically something that could work by me simply creating links between different articles on a separate module settings page, so I don't have to enter into the EDIT mode for each article to add the connection.
You can set up nodes to be used like taxonomy items.  Take a look at this:  https://www.drupal.org/project/entityreference

That module will allow you to set a content type as the source for cross-linking nodes.