Problem in nose? Sinus infections often relate to inadequate air passage to the nose. Assuming the problem is architectural – like a deviated septum or enlarged turbinates -- some people are often sentenced to many recurrent infections until those structures are corrected. Consult with a nasal specialist to see if the problem is nasal. Blockages can lead to the sinus woe. Ct scan, a type of x-ray, may help.
Chronic sinusitis. You may have chronic sinusitis which is an over active immune response, or recurrent acute sinusitis, which is bacterial or viral. If the symptoms persist ask you doctor for a referral to an otolaryngologist for examination. They may order a ct scan to visualize the sinuses before suggesting a course of treatment.
Relapse. Sinus infections often require more than the usual 10 days of therapy and symptoms may come back in a few days if the initial treatment was not given for long enough period of time. Your symptoms should be gone for several days before stopping the medication.
Not unusual. You may be dealing with persistent post nasal drip an inflammation. See your doctor. There are ways to manage both without necessarily putting you through another course of antibiotics.