My daughter is always coughing especially at night but the pediatrician said it is nothing to worry about? it makes her vomits at times too

Cough: "Always coughing, especially at night" is not normal and could signal asthma and/ or allergies. Try removing any dust collecting article form the your daughter's room and replacing carpet with tile or wood floors. Ask your doctor about allergy and asthma.

Possible reflux : I would talk to her doctor about the possibility of gastroesophageal reflux causing her nighttime cough and vomiting, also limit food intake for 2 hours prior to bedtime.

I agree with both : answers. Your daughter needs Pulmonary Function Tests to determine if she has asthma, then a medical decision about evaluation for gastro-esophageal reflux. I suggest you return to the primary healthcare provider & request these evaluations politely, but firmly.