The World Health Organization and CDC's website confirm that a running nose and sputum occur during a cold but they don’t rule out coronavirus.
The symptoms of the novel coronavirus as described by the Centres for Disease Control and Prevention (CDC) does not include a runny nose and sputum secretion. Therefore, these symptoms do not necessarily mean that an individual is infected by the coronavirus as they commonly occur during a cold.
The COVID-19 pandemic has given rise to a lot of potentially dangerous misinformation. For reliable advice on COVID-19 including symptoms, prevention and available treatment, please refer to the World Health Organisation or your national healthcare authority.