Two-step decision angle: in IMNCI you decide HOW sick and then WHAT to do, and both parts matter for the answer.
How sick: in a 2 month to 5 year old, cough or difficult breathing plus lower chest wall indrawing is classified in the severe band (severe pneumonia / very severe disease). This is a red category that must leave the PHC.
What to do: the protocol for a severe classification is not bare referral. You give the first dose of an antibiotic right there, so the child is already covered while travelling, and then refer urgently to hospital where oxygen and monitoring are available.
Reject the others. Antipyretics only ignores a potentially serious lung infection. Antibiotics with home follow-up is the action for the milder pneumonia (fast breathing without indrawing), not for indrawing. Refer without giving an antibiotic wastes the chance to treat during transit. Hence the combined action, antibiotics plus urgent referral, is correct.
Ref: IMNCI Chart Booklet, Government of India / WHO.