A 7-day-old female infant born to a 28-year-old primigravida mother presents with poor feeding and excessive crying. The mother reports severe pain in the left breast during feeds, with visible erythema and a palpable lump. Examination reveals a tender, indurated area in the upper outer quadrant of the left breast with purulent discharge from the nipple. The infant's weight has dropped 12% from birth weight. What is the most appropriate immediate management?