1. It's taking you to your shop home page strictly because that's how your site has been set up to handle 404-not-found conditions.

2. The fact that going to the login.php directly works shows that you've got the files in the right folder.

3. The reason going to just /shop/my_admin/ gives you a redirect is because when you don't specify a filename, the server assumes index.php and, since the first thing index.php does is verify whether you're logged in, since you're not yet logged in, it's trying to redirect you to the login page. Hence the difference between going direct to the login.php page yourself.

4. Your redirects are clearly the problem, and the admin redirects are always built based on the info in your /admin_folder_name/includes/configure.php file.

So ... your edits to the admin configure.php file are your problem.

Please post what you have in your admin configure.php file now. Feel free to mask the actual admin foldername and replace your URL with my_domain.com. And of course your database details.
Please don't mask anything else.