Meaning of "He went ‘Eeeeee!’ high up in his skull"

Question

This text is from The Children's Bach by Helen Garner:

Billy drew a breath and started to scream in short, sharp cries. He flung himself back on Dexter’s lap; he clapped his left hand over his ear, and bit into the heel of his right hand, held it against his large crooked teeth and pressed, pressed. He went ‘Eeeeee!’ high up in his skull.

Does it mean: He made a sound like "Eeeeee!" that echoed in his head?

Or does it mean: the sound like "Eeeeee!" that he made was deafening?

Answer 1

It means the former: he screamed "Eeeee!" in a high voice that echoed in his skull. There are six main areas of vocal resonance in the human body. Of these six, one is the upper skull. In speaking or singing, the skull cavity is used to produce very high vocal pitch. Billy's shriek is therefore high up in his skull.