Hello,
Thanks for posting your query.
Throbbing headache can occur with fever in certain viral or parasitic infections caused by insect bites ( eg malaria , dengue etc).
However it can occur in otherwise non insect borne viral or bacterial infections as well.
The treatment with a broad spectrum antibiotic seems appropriate however if analgesics ( like acetaminophen)are not able to control his headache then the doctor should try an alternate analgesic ( ibuprofen, newer Nsaids etc).
If it persists then further investigations need to be done like blood counts and smear ( for parasitic or viral infection) , blood pressure ,fundoscopy ( for intracranial pressure changes) etc.
As of now since its been a week already and rest of his symptoms have resolved with antibiotic therapy it is still most likely that the headache will resolve in a couple of days ( usually 7- 10 days since onset) .However if even after appropriate analgesia , it worsens or patient develops any new symptom like neck stiffness, vomiting , blurred vision etc then it's best that you get him reevaluated immediately for ruling
out any complications like blood pressure disturbances , migraine , encephalopathy or neuro -vascular complications .
I would say that if there is any particular history of travel or suspected insect bite then the most appropriate thing would be to get him rechecked and repeat tests if required since in some insect borne illnesses the symptoms and blood tests may considerably change over a week .
If there is no definite history of insect bite then it could still be a bacterial infection which has partially responded and should resolve in another few days (3-4).
Hope I have answered your query.
I'll be available for any follow up queries .
Regards

---