My 1 month old has a cough. The doc said it was no more than a slight cold but its getting worse. Sneezing too. No fever or distress.?

See below. It is possible that the cough is from a cold. Often the cough is due to nasal secretions and good irrigation may help. If symptoms continue or worsen you should return to your doctor as the cold can progress. You should be concerned if baby develops fever, flaring of the nostrils, very fast breathing, or pulling in of the ribs with breathing.
URI. Simple irrigation of nasal passages by saline nose drops e can help to reduce symptoms.
Sneezing. Sneezing in newborns is a way to blow therir nose. They breath thru' their nose (not mouth). As they grow , develop more, start eating solid food, and have more tone in their neck muscle then they breath thru' mouth and sneeze less.