How long after being born will baby show the symptoms of HIV if he or she is infected?

Highly variable. Baby may not show actual symptoms for some time, or may be born with significant problems.
Get tested. Many states perform HIV testing on all newborns, and some states require that the mother be tested during pregnancy, otherwise the baby is tested before being discharged from the hospital. All pregnant mothers with HIV should be treated so they can reduce risk of transmitting HIV to the newborn. A baby can also be tested at any age (even a few hours old newborn). When in doubt get tested!