A random dictionary search for "egotism" turned up this:
egotism [ˈiːgəˌtɪzəm ˈɛgə-]
n
1. an inflated sense of self-importance or superiority; self-centredness
2. excessive reference to oneself
I'm sure that there is some word to describe the complex which you described, and it might even apply to Chihaya's sister, but I don't see yet that "egotism" is by definition a word that applies to her.
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