Cough along with Cold and fever most of the time is a  viral illness or allergic and it needs supportive care along with proper hydration needs to be maintained. you can give steam inhalation which may be useful . cough needs to be treated with medicine like anti allergic  expectorant bronchodilators antitussives or cough suppresents medicine which should be given only after a proper evaluation by the doctor according to the type of cough and need. In severe cough nebulisation can be given where medicine directly gets dilivered in the respiratory tract. Also if fever is there paracetamol can be given to reduce the fever and the dose is 15 mg/ kg body weight and can be repeated after 6 hours again if required . Home remedies like Tulsi & ginger mix in honey can be tried for soothing.

Most of the time cough cold, fever  are viral in origin, it may subside by 3 -9 days.  No need of any medication if mild.   If fever above 100F then need fever medication  (paracetmol) as per weight.  If baby have cold then need steam inhalation, nasal decongestant drops (nasivion baby nasal drops/Otrivin-P nasal drops 1drop in each nostril 3-4 times a day for 3 days).  If cough then need cough syrup or drops as per babys cough condition  (wet or dry).  Keep ur baby well hydrated in cough cold fever episode Maintain hygiene, hand wash properly,  Keep ur baby away from other infected persons if possible , continue to give  all  food items as before, It will help for fast recovery.   If decreased oral intake, decreased urine output,  breathing difficulty,  Then need to consult with ur nearest pediatrician

Please write the weight of baby.