Near hyperventilating, she sat heavily on the couch and clutched her head with her hands.
Near hyperventilating, she bent over and drew in deep breaths until moonlight revealed the dismembered hand near her feet.
Hello,My ten-year-old Terrier/Spaniel is hyperventilating and she keeps coughing.
She sensed Rhyn's presence before any of the others and braced herself, almost hyperventilating.
I think what you're describing as hyperventilating is more likely gasping for breath.