Category and Product Pages Not Secure/(Saved as External Links?)

My Category and Products pages open as non-SSL pages. All other pages of my site are secure (HTTPS). My hosting service told me that the Product and Category pages appeared to be set up as external links.

My includes/configure.php and admin/includes/configure.php files seem to be set up correctly. Below is a snapshot of a part of my admin/includes/configure.php file:

If you desire your entire admin to be SSL-protected, make sure you use a "https:" URL for all 4 of the following:
*/
define('HTTP_SERVER', 'https://mysite.com');
define('HTTPS_SERVER', 'https://mysite.com');
define('HTTP_CATALOG_SERVER', 'https://mysite.com');
define('HTTPS_CATALOG_SERVER', 'https://mysite.com');

// secure webserver for catalog module and/or admin areas?
define('ENABLE_SSL_CATALOG', 'true');
define('ENABLE_SSL_ADMIN', 'true');

What you (they) are suggesting has nothing to do with external links.
Any page that contains a link off the site will drop the https
Had you provided a link, we might have been more helpful.
Normally, you would not want an entire cart to be secure. That's because many cart link to offsite info. That link will drop the https Having the log in and checkout secured IS recommended.
Curious as to the host.

That makes sense. Thank you for taking the time to help a novice.

GoDaddy provides my hosting. I've found that some of the people on their service desk are knowledgeable. Others are not.

My site is https://www.sirsmicro.com

Thanks again.

"GoneDaddy" has you totally on the wrong track. Unfortunately, that's not uncommon.:no:
You may note the GoDaddy is conspicuously missing from the recommended hosts page.

You need to compare your config files to the originals. If you're not familiar with how to do that, you could paste a copy of each of your configure.php files here. Be sure to change the username and password to ******** before you paste it.