You may need to check the contents of config/site.php to see if there's a base URL specified in there. That would need to be changed.

It's also possible that you have rules in your .htaccess file that might need altering.

You should turn off and clear the cache before making any changes. Once they're OK, then turn the cache back on.

If you're using cPanel hosting, you should find that you already have a free SSL certificate. If not ask your hosting provider to turn it on for you. Free certificates are also available from LetsEncrypt.org