Immunity against common cold. Nose?

The way  you describe it so far  the sneezing doesnt seem cause for concern and no medication is needed . However if other symptoms like fever , cough , vominting , fast breathing or feeding difficulty develop you must go to a Pediatrician for a physical check up . As far as the immunity query : After birth till about 3 to 5 years of age a newborn baby is exposed to about 5000 viruses . And immunity develops as he is exposed to them and antibodies develop within him . Most of these viral infections are self limiting and spontaneously subside and may only require symptomatic treatment for fever , Nasal  discharge etc . Generally we refrain form giving antibiotics for seemingly viral infections as they cause more harm rather than good