Please Contact customer service and ask them to unlink your account.
Also signed in my sons computer with my account. So had to figure out how to change users.
The re-install didnt work for me either.
What did work was simply signing out of my user account on windows.
Then when I went to skype, it diverted back to the skype login.
Good luck finding the log-out message from settings, But it should work.
Install Skype Desktop, which will allow two features:
here are two options:
Watch this YouTube video to see how to log into the Skype website and download Skype Desktop.
Not everything the video shows will be exactly your experience but it's very helpful for navigating and installing.
Or you can just goto http://www.skype.com/en/download-skype/skype-for-c
This will provide you the most current desktop version to install, which allows multiple user login.