Whoah some administrator should look into that random account.
One reason, definitely, that these high notes don't come out is because of condensation (and saliva?) in the bore of the instrument. There was this while I was wondering why I could not scream out an altissimo D. (In Whitacre's "Gawd$illa Eats Las Vegas".) Turns out that it was the water. Another time was just a high G... stupid water. And that was Holst's "Mars" form The Planets. (If you know that piece, you'll know why not being able to play that note is so tragic.) So when you're performing, make sure you swab whenever you can.
Anyway, I suggest NOT turning the head inwards. I would turn outwards, actually. And make sure you use support. I don't suggest "smiling", or tightening the lips, although many experienced players would beg to differ. Keep the air intense, but not tight. That would require a strong embouchure, though. Don't count on it, I have an embouchure very different from your standard piccoloist.
The flute family: probing the lower limit of human hearing and the upper limit of human tolerance.