I have used SharePoint in the past but just as a user not as an admin and now I am in charge of running SharePoint at my organization. I was asked to go in and update a link on the main page and since I made the change only a seemingly random list of people can see the change.

when I log in as another user and check out the page from the all files list it pulls up the edited page.

I have spent days pouring over every article I could find that sounded like it might sort of maybe be about what im going through but I have not found anything that remotely describes my issue.

Hi,

From your description, only  a few user can see the changes of the page.

For your issue, I suppose that you are editing a page which is a publishing page.

It is by default that only the user who can edit items can see the draft pages.

So after you edit the page, checking in the page and publishing it as a major version.

After doing this, people with read permission can see the change of the page.

Hope it helpful. If there is any problem, feel free to reply back.

Best Regards,

Lisa

As mentioned by Lisa, I would also check the permissions. 

I believe, the users who can see have approver rights. 

Please make sure that the page you edited is checked in and published with a major version. That should allow everyone to see the changes you made.

Thanks,

Ved