First you can ask for a CRP test. This is simple blood test that can measure your levels of the inflammatory marker. It is not usually done on people who have sinus problems because it is designed for heart disorders. Although it still has been proven useful for chronic sinusitis.
Ask your doctor what the high levels or low levels of your result mean. Higher levels of CRP test mean a bacteria infection which require antibiotics, while low levels mean its viral and time is the only cure.
You can also ask your doctor for a CT scan. A CT scan of the sinuses have been shown to show patients that have a chronic sinusitis instead of chronic coughs. This misdiagnoses is simply caused because doctors fail to realize that the chronic cough is being caused by th sinusitis rather than something else. Leading to possible wrong prescription medication.
Don't be afraid to ask your doctor for other alternative testing. If you do not feel comfortable with their answer go and get a second opinion, even a third if you have to.