Series is and about a girl that grows a pair of demon horns over night.
Mom reveals there's demon blood in the family on dad's side, and just comments that her destiny to find and defeat the magical girls must have kicked in.
Cute hilarity ensues. Shamiko finds out that Momo at school is a magical girl, and her pathetic attempts to "vanquish" Momo end up endearing them to each other.
Much yuri bait, very recommend.
Momo ends up relying on Shamiko for her emotional energy. She is emotionally dead and depressed, suffering PTSD due to her responsibilities as a magical girl. Hence this recharging hug.