How to stop Google search, by using “noindex” and “nofollow,” from offering options to private pages on a website


I have a family history website, call it "my_family.com". The primary file, index.php, has some introductory remarks of explanation and an html form into which one puts the website’s password (there’s a single password used by all family members). If one runs "my_family.com" and inserts the correct password and clicks on the "Submit" button, the php code in the file takes you to the first of several html files — call it "first.html," which gives one links to further html files. All of these files contain family trees, copies of letters, photos, reminiscences, obituaries, etc., and none of which should be available to non-family-members. I soon found out found that if one put the phrase "my_family.com" into the Google search window (whether on computer of smartphone), one got a list of options, not just a Login option but about eight to ten 3-4 word excerpts from html files on the website; and if one clicked on any of these latter options, one bypassed the password process and was taken directly to other files on the website, i.e., files that should never be publicly revealed.
What I’ve done to avoid such access is to create a cookie in the original index.php file. If the user inserts the correct password, the cookie is set to "passwordCorrect" Each subsequent html file then checks whether the cookie has that value before the user is allowed to move on Putting in the cookies has solved the problem of public access, but nevertheless a Google search still shows the 3-4 word excerpts. I have tried to stop Google search from doing this by putting into the header section of first.html: ”” (without the outer quotes). But that has been in the file for about three weeks and has proved useless. I tried using Google Search Console to get Google to make an early "crawl" of the file my_family.com, but am frustrated by the lack of examples about how to use it, and don’t think I succeeded. Maybe I should be asking for a crawl of the file my_family.com/first.html, instead of the basic my_family.com website? I’d appreciate any advice anyone has about this. For example, how do I determine when the last crawl was, when can I expect the next crawl, is the meta tag in the correct file, etc? Thanks