dto, this is the kind of psychological analysis that I'd love to see, backed with documentation, at the Supermanica entry devoted to Supergirl --it would do Fleisher proud.
http://www.supermanica.info/wiki/index.php/Supergirl Donning a Supergirl costume was a desperate attempt to gain acceptance by the only other known Kryptonian survivor, and one might argue that Kara was acting from Day One -- trying to make a good "first impression" upon arrival on a strange world.
But learning that Superman was actually a close family relative must have been another (albeit welcome) shock. Since Kara was so anxious to gain Superman's acceptance, this must have left her extremely vulnerable to suggestion, as she wholeheartedly accepted all of his instructions and conditions. And being so terribly lonely as the Last Daughter of Argo City, Kara was determined to fully integrate with human society, being with her orphanage peers. Perhaps in these early years, Kara's continued masquerade as Linda helped keep her mind from revisiting those horrible last days of Argo City. Even when her real parents were recovered, Kara was still emotionally scarred by those memories -- unlike Kal-El who mostly could not recall personal memories of Krypton's destruction.