You have a hidden infection in your paranasal sinuses and this is descending downwards and infecting your throat causing the hacking cough and fever. Unfortunately, your nasal septum( the central plate of bone separating both your nostrils) has overgrown crookedly and this has resulted in one nostril being narrow and the other roomy. This roomy nostril is unable to filter the inhaled air, which has allowed infection to enter your sinuses and throat! Also, medication which need to be administered through the nostrils as sprays cannot be given due to the crooked septum.
Next Steps
You need to Endoscopic Nasal Surgery to correct this crooked nasal septum and then subsequently, undergo a few months outpatient treatment for your sinusitis.