My 6 week old has a cough that causes her to gag, not be able to breath and throw up?

Should be checked. Whike this could be reflux a common condition in babies, it could be several other things that are potentially more serious.
PROCEED TO DOCTOR. Any cough in a 6 week old is concerning. However, one that results in vomiting should immediately be evaluated by a pediatrician. Is the infant having any other signs of respiratory distress - chest wall sucking in (retractions) with breathing, fast breathing, nasal flaring. Any fevers. Your child should immediately be seen (er if no clinic open).