A little bit of milk spitting up when the baby sneezes or coughs is normal. Discuss medications with your doctor. For symptomatic relief use saline nose drops like nasoclear or nasomist, give the baby steam with a safe steam inhaler and have a diffuser in the baby's room with eucalyptus oil.

a one month old baby cannot be given any cold medicine. try home remedies, nasal saline drops . for the vomiting I would suggest you get your pediatricians opinion. is it spitup or actual vomiting?