1. the child has proved pneumonia on CXR
2. the child has suspected/verified pertussis
3. the child was exposed to histoplasmosis, aspergilosis, etc
4. the child has been diagnosed with cystic fibrosis
5. the child has known sickle cell disease and has fever and chest pain
6. the child is immunocompromised and does not take prophylactic antibiotics, or - prophylaxis is being taken, but now the child develop also fever
7. the child has hx of exposure to TB and positive tuberculin/equivalent test
The use of antibiotics is not appropriate for the common cold, most viral infections and uncomplicated influenza with no other underlying disorder or risk factors.
This is not entirely complete answer, just a few points to start considering
As always, good thorough history including EPIDEMIOLOGIC history (traveling, contact, immunization status + exposure) and physical exam will lead to correct diagnosis and treatment in > 95% of cases considering that the MD is not forced to practice assembly line medicine (= 15 minutes with computer and 3-5 minutes with patient and parents). Any more questions? Feel free to ask.