My daughter has thick cough with no phlegm and also colds. what antibiotic should she take?

If Viral, none: Colds are caused by viruses. Antibiotics do not treat viral infections. Antibiotics are for bacterial infections. Instead of antibiotics, treat cold with supportive care. If daughter is over 1 year of age, try using honey for cough. Salt water drops can help to relieve nasal congestion. Also avoid multi-symptom preparations as they are not recommended by American Academy of Pediatrics.