& the throwing up could be from a cold or ..... could be a simple thing like needing to switch formula ;)
Take her to her pediatrician , baby's can get whooping cough & it's very dangerous to infants . Not saying that it's that , but just take the precautions . I think the sneezing is normal at first when they are born, my baby boy is 2 weeks now& he sneezes also .
I would say since shes just a month old i would call her doctor and talk with them. Theres not much you csn give them over the counter being so young but the doc may tell you something that could def work. Especially since she throws up evrrytime she eats. Does she have a fever?