With a common cold, the nasal discharge can be different colors, causing some confusion. It initially starts out clear for a few days (looking just like an allergy), before turning whitish or green and then back to clear again as it resolves over a week or two. There may also be a little bit of fever, known contact exposures with others who have colds (very common for children in day care), and perhaps some swollen glands in the neck. A cold happens at any time, usually without a pattern. The inside of the nose looks red and inflamed. The symptoms of infection simply have to run their course. Cold medicines do not shorten this viral infection. Antibiotics are not routinely needed unless there is a complication of the cold like an ear or sinus infection.
With allergy, there's often a family history of some type of allergy and possibly some seasonal pattern ("This happens every spring."). The signs and symptoms include sneezing; itchiness about the eyes, nose, or roof of the mouth; a crease across the top of the nose from rubbing the nose repeatedly ("allergic salute"); mouth breathing; and dark circles beneath the lower eyelids. The inside of the nose looks pale rather than red, and these symptoms often last longer than the 10 to 14 days seen with a cold. Allergy medicine, like antihistamines, may offer some relief, but is not a cure.