If you share a computer with someone else who is also a Yahoo! Music/ Yahoo! member, that other person may have been signed in when you visited Yahoo! Music. This means that you will have to sign out the other member and sign in as yourself.
Click the "Sign Out" button on the upper-left side of the home page. The welcome message will change to "Welcome Guest," and you will now see a "Sign In" button. Click this button, enter your Yahoo! ID and password, and click the "Sign In" button.