If your 2-year-old child has been coughing for 3 weeks, it is important to try to identify the cause of the cough. It could be a lingering cold or possibly allergies. In some cases, coughing can be a result of post-nasal drip, where mucus from the nose drips down the throat, especially when the person is lying down, such as at night. In this case, nasal hygiene with a saline solution can help alleviate the symptoms. It may be worth trying this approach to see if it helps alleviate the coughing.