I originally made both Kokytos and the ice demon nation, which were suppksed to be from Kokytos. I don't know if Trapezoid's 'Kyotos' is just an alternate spelling or supposed to be different.

In any case, I didn't think we were going to use any of the story from last RP, which has already lead to another contradiction. 'Cocytus' is a river of the Underworld in Greek mythology (not an icy hell) and Moggotheddon's story obviously borrows from said mythology. In fact, I think I mentioned somewhere that he was drowned in the Cocytus before being thrown into Tartarus.

So now we have three very similar names for what may or may not be the same place (we could always say the Cocytus river simply runs through Kokytos, I guess), and the three are almost entirely disconnected in the story.

To avoid confusion and unnecessary complexity I suggest you just be vague with Emily's background. Say she was sent to some other frigid world, leaving out small details like its name or that it was in the Underworld. That way our stories don't have to contradict.