I would give Bryonia a try, because the cough is painful, the baby cries each time she coughs, Bryonia has hard coughing and vomiting from coughing, and must sit up to cough, so... it may be worth trying in a 30C, twice a day for 2 days, unless it makes her worse, in which case, stop giving it and let us know; and, no, I wouldn't withhold milk from a baby, I'm sorry, it just doesn't make sense.

Snoopy