if it is always cough followed by vomiting it's normal. happens to all my three kids. when they are unwell esp when they are coughing they will vomit it is because the strength they use to cough will result in vomiting. so usually I will prepare a bucket with plastic beforehand in any case they become merlion. try to give warm milk or water and not room temperature. I usually dilate the milk if you are using FM. and apply baby vicks at the chest area. hope your LO get well the soonest.
Siti Haniza