Actually, most allergists no longer go by the color of the drainage to identify sinus infections. It used to be green, yellow or grayish drainage was considered to be a sign of infection. And both bacterial and viral drainage can be any of the colors. Clear drainge often occurs with a cold, which is viral. White drainage has a high leukocyte component, which is a sign that your body is fighting off something.
You can have a sinus infection with no visible draignage - IMO, the worst of the sinus infections and the one I have most often. I call it concrete head. It can also cause migraine type pain.
You have four pairs of sinuses - the pair in your forehead, the pair in you cheeks, a pair that is under the center part on the top of your head ( a lttle lower, but hard to describe) and another pair below that. It is possible, and quite common, for you to have infection in one or a pair of sinuses and not in the others.
The doctors are really trying to avoid overusing antibiotics like they used to do. It is possible to get over a mild sinus infection without antibiotics, but when you are resorting to extreme measures, you need to see the doctor.