Character vs self.
In the passage Millicent has just gone through one of the initiation tasks. The passage describes her as coming out of a basement room that was in complete darkness. The only light she sees is when she is let out of the room. Since this is an initiation and not mandatory imprisonment, Millicent has the ability to leave the darkened room so she is not going up against any external forces like other characters, nature, or society. She must battle the dark solitary confinement on her own. This is an internal character vs self conflict.