About the "square sky", I'm thinking she means the sky that she sees when she's in the city. She has used this reference a couple of times in other songs as well.
UNITE!
Quote:
同じ朝が來るのが憂鬱で 急に
四角い空とても むなしく見えて
Melancholy at the same morning coming again Suddenly
The square sky seems so empty
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Greatful Days
Quote:
ビルの隙間から いびつに尖る空
いつか見た空は 果てなく広かった
Between the buildings, an irregular sharp sky
The sky we used to look upon, was endlessly wide
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I guess the "square sky" comes from the obscuring from the buildings in the city. When you stand in the streets and look up, the sky may appear framed into a square by surrounding buildings. From ayu's lyrics, it seems to give a sense of being enclosed and trapped, I feel.
And about the desires, I think she means
she is filled with those desires, not the sky.
Just my opinion, though. We can only guess until ayu herself clarifies it (which she almost never does lol).