You need to make sure all of the elements on your website were also updated from http to https. This could include some of the following:
- Images on the page(s)
- JavaScript, css files, third-party fonts
- Tracking scripts and tracking codes
If you're using WordPress, I'd recommend installing a plugin called
Better Search Replace. Make a backup of your website's files and database before running it.
When you're ready to run the plugin, search for
http://yourdomain.com and replace with
https://yourdomain.com (select all of the db tables in the list).
I'd also recommend that you still get an SSL Certificate installed on your origin server and then updating your Cloudflare settings from Flexible to Full/Full (strict). As your webhost if they support Let's Encrypt or if it's available and to run the check on your account.
Hope this helps!