Question

Shannon goes to the doctor complaining of symptoms of a sinus infection. She has frequent headaches around her eyes and complains of dizziness. Why would her doctor ask for details of her family medical history if Shannon believes she only has a sinus infection?

Answer 1

Because, Sinus infection is generally diagnosed based on patient history..
http://www.medicinenet.com/sinusitis/article.htm

Answer 2

A doctor might check with their history to maybe pinpoint the cause of the sinusitis.

We know that it's caused by pathogens, like bacteria.

But there are certain conditions that make it easier for someone to develop sinusitis, like cystic fibrosis.
Since these tend to run in the family, a doctor would check the patient's family history.

And before prescribing antibiotics and sending the patient on their way, a doctor might want to make sure that it's not "chronic sinusitis."
"Chronic sinusitis" is the kind of sinus infection that stays for a long time. If someone has chronic sinusitis, they may need to be referred to a nose/throat specialist.

Knowing the patient's personal and familial history of headaches and dizziness would help too, just to rule out the possibility of brain cancer.