Symptoms of allergy typically occur when exposed to something in the environment to which you are sensitive, for example, Aunt Bea's new Himalayan cat, or ragweed in the schoolyard. Symptoms tend to clear-up once the environmental culprit has been removed. For some, allergy testing and shots may be needed to resolve the problems. Colds are viral infections that usually occur after exposure to someone else who is sick. The symptoms, while similar to sinusitis, last only about a week.
Antibiotics have no role in treating common colds.
Sinusitis differs from cold or allergy by being a bacterial infection causing swelling, congestion, and drainage from the nose and sinuses. It typically arises after a cold and manifests itself by symptoms of the cold that simply don't get any better. So rather than the headache and congestion going away after a week as with a cold, they drag on and on and on. It's this duration of symptoms that signal it's time to see a physician to get treatment. In addition to discussing your symptoms and performing a careful exam, your UNC ENT doctor may wish to obtain x-rays to confirm the presence of sinusitis.