wp-admin redirects to subdirectory after moving installation to subdirectory

I have moved a wordpress installation to a subdirectory, from var/www/html to var/www/html/wp-blog mainly to make it future proof. I have followed the instructions in the codex. My server is configured as such

1. I have a nginx reverse proxy which directs calls to blog.mysite.com to the port 8080.
2. Apache listens on 8080
3. I have modified the .htaccess from what is given in the codex and it is as follows

.htaccess

IfModule mod_rewrite.c
RewriteEngine on
RewriteCond %{HTTP_HOST} ^blog.mysite.com$
RewriteCond %{REQUEST_URI} !^/wp-blog/
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ /wp-blog/$1
RewriteCond %{HTTP_HOST} ^blog.mysite.com$
RewriteRule ^(/)?$ wp-blog/index.php [L] 
/IfModule

I have only changed the ^(www.)? test to blog since I don't want www. Also although the wordpress instance is in a subfolder I would like to server it via blog.mysite.com and the admin at blog.mysite.com/wp-admin.

Now my trouble is that when I use the the url blog.mysite.com/wp-admin it takes me a the login page but I get stuck in a loop after that. I noticed that my url in the address bar has a redirect_to set at blog.mysite.com/wp-blog/wp-admin. If I remove wp-blog from the redirect url, I am able to login.

The weird part is that, if the session gets over while I am in the admin page, the redirect url is fine!

At this point I have changed the Wordpress URL in the General Settings to blog.mysite.com/wp-blog and everything works as far as I see. But as I said before I would like to use the admin panel on the root.