Answer: Give antibiotics and refer to tertiary care.
Step 1: Under IMNCI, a child aged 2 months to 5 years with cough or difficult breathing is assessed for danger signs and chest indrawing.
Step 2: Lower chest wall indrawing classifies the child as SEVERE PNEUMONIA or VERY SEVERE DISEASE (in the older IMNCI cough chart). This category cannot be safely managed at home.
Step 3: The IMNCI instruction for this category is to give the FIRST dose of an appropriate antibiotic and then refer urgently to a hospital. Antibiotic before referral covers the child during transport, and urgent referral ensures higher-level care (oxygen, monitoring).
So neither antipyretics alone, nor antibiotics with home follow-up, nor referral without a first antibiotic dose is correct. The right action is give antibiotics AND refer.
Ref: IMNCI Chart Booklet, Government of India / WHO.