Just before I made this post, I kept on experiencing a loop in my WordPress. I cannot access my dashboard and every time I go to my Login-In page, it keeps on going back to my home page. So If you keep on getting an error as shown below after your WordPress Upgrade :
No Update Required Your WordPress database is already up-to-date! Problem After WordPress Upgrade
You need to reboot your server. Just for your information, I am using Dreampress and I do have VPS account with Dream host. Based on my research this might be because of the Varnish Cache.
Just sharing what I have experienced today, you might be one of those having the same problem.