You should be able to see all of your own Protected Posts on your private site.

As for your public site, only the people on your Protected Lists can see your Protected Posts on that page... and only when they are signed in.  For more information, please see:

Who can read my Protected Posts?
http://help.xanga.com/whocanreadmypp.htm

Do I have to be signed in to read Protected Posts?
http://help.xanga.com/signedintoreadpp.htm