Final answer:
A subconjunctival hemorrhage can occur due to forceful coughing episodes. Treatment for pertussis typically involves macrolide antibiotics for both the patient and close contacts.
Step-by-step explanation:
A subconjunctival hemorrhage in a patient with nasty coughing episodes is a condition where there is bleeding in the space between the conjunctiva and the white part of the eye. This can be caused by the forceful coughing associated with the coughing episodes.
As for the likely cause of the subconjunctival hemorrhage, it is not specifically mentioned in the question. However, since the patient has nasty coughing episodes, it is possible that the hemorrhage is caused by the strain of the coughing.
Regarding the treatment for pertussis (whooping cough), a macrolide antibiotic like azithromycin or clarithromycin is often used for both the patient and close contacts to prevent the spread of the disease.