Manually Set Post Categories

Hey, this one is a bit complicated to explain so I have broken the post down into pieces so you can skip ahead.

1) Background
2) Problem
3) Question
4) Source Code

== Background ==

I am in the process of creating a simple script that will pull a pre-defined column from a non-WP table and adding it as a POST to the wp_post table. Also, it is supposed to fall under a user selected category so when the end user browses the site, they can select a category and see all the newly imported posts.

== Problem ==

I am updating the wp_term_relationships table to match the wp_post.ID to the wp_term_relationships.object_id so that the new posts are created under the proper category. However, when I browse the site by category, all the new posts will fall under the correct category, but using any sort of paging or sorting fails to detect the new posts.

== Question ==

Is there a step or item I am forgetting to update in the database to make the links work, or should I be using a custom template function to make the paging/sorting work? I would like to on the single.php template have it so you can see the name of the next and previous posts within that same category sorted alphabetically by post_title, and then click on the links to actually go to the respective post.

== Source Code ==

Not sure if this is okay, but here is a pastebin.com link to the functions.php script I am writing containing all of the SQL code.

https://pastebin.com/f2a678a71

Before I forget, thanks for taking the time to read this and help me out as I am still new to WordPress and am trying to learn the ropes.