Excuse me a moment while I completely contradict myself... After taking another look at those pages, I think this is what actually happened:
Mei was attending a performance by Akane and Rinna's idol unit - no, changed my mind about that - Mei stumbled upon Rinna lying unconscious on the floor. She helped out somehow, maybe by calling a first-aider to the scene. (Or maybe by employing some healing skills she picked up herself when spying on the A+E staff to ease her boredom? This part is completely unsupported, by the way.) Akane was grateful to Mei for saving Rinna, and the "special someone" photo was her reward. So there's no particular reason to suppose Akane and Mei previously knew each other, especially as Mei immediately denies it, or would have done if they had given her a chance to get the words out.
As for Rinna, she learned that Mei was the one who saved her, and enrolled in the same school in order to be near her, though she clearly wasn't expecting to be quite so near as she ended up. It's a little odd that Mei doesn't seem to recognize Rinna, so presumably she isn't a fan of the idol unit? And goes out of her way to avoid knowing anything about them? Or selective amnesia is a symptom of her condition? I hope that gets clarified, because it's bugging me now...
And as for Akane, I don't think she's going to be important to the story after all. Not to extend the love geometry, at any rate. And Rinna effectively fills the transfer student role, so that's out too. So much for the glasses and braids...
