John heard a woman shriek downstairs.

[alpacinou]

Is this correct and natural?

John heard a woman shriek downstairs. It was as if her screams were creeping up inside him. The hair on the back of his neck stood up as the wailing got louder.

 

[Charlie Bernstein]

Maybe. Creeping is slow. Wouldn't you react suddenly to screams?

 

[emsr2d2]

Your first sentence suggests to me that the woman shrieked just once. That doesn't fit with "her screams". If you change "shriek" to "shrieking", it works better. That suggests the shrieking was of a longer duration.
Like Charlie, I don't like "were creeping up inside him" at all. Perhaps her screams "penetrated to his very core".

I think you've tried too hard to avoid repetition. Was she shrieking, screaming or wailing? They're not entirely the same.