See your doctor to evaluate coughs that won't go away or get worse after a respiratory illness. Don't expect antibiotics, but know there are other treatment options. After many upper respiratory viruses, coughs will linger, sometimes for up to six weeks. A cough that is not managed with over-the-counter medicines should be addressed by your physician. Coughing all day long at school or work (or keeping up your spouse with coughing all night) is not a good plan.
What can your doctor do? First of all, he or she needs to rule out any secondary infection such as a pneumonia. More commonly, you may have developed some over reactive airways and may benefit from some inhalers or other asthma-style of medicines. A prescription cough syrup used at night may help with the nighttime exacerbations, and your doctor can remind you of some traditional home remedies such as cool mist humidifiers that may help.
Finally, sometimes a cough comes from other sources, such as acid reflux or sinus drainage, which require different treatments.