It is normal for a child with running nose and cough to have decreased oral intake,giving her warm liquids will help,noisy breathing during cold is normal but not normal if she snores without cold and has mouth breathing we need to rule out causes of nasal obstruction like adenoids,cough can be of various types it is always better to use it on pediatrician advice as there is no uniform cough syrup.
Next Steps
Wait for 3-4 days as long as the child is comfortable visit the doctor if child has breathing problem,feeding problem or associated with fever
Health Tips
Cough is good as it helps the child rather than harm,it helps to remove excess mucus secreted in airways or is a symptom of swelling in airways resulting in narrowing and irritation resulting in cough and breathless.I would recommend warm water with honey as a good home remedy for cough.