Is subconjuctival bleeding a complication of whooping cough ?

Whooping cough: Yes s a subconjuctival hemorrage is often seen with whooping cough

Possibly: With whooping cough you have coughing spells that do not stop. If you cough hard enough and persistently enough you could end up with subconjunctival hemorrhages. So it is not directly related to pertussis but is a complication of coughing a lot and hard.

Could be: Forceful coughing or vomiting can increase the pressure in the blood vessels of the neck and head structures. Fragile capillaries in the eyes frequently rupture, creating small hemorrhages. Petechiae are microhemorrhages under the skin, often seen in the face. They typically heal up on on their own without intervention and pose no long term consequences.