Step 1: Interpret the Benedict's test clue first.
Benedict's reagent turns positive with REDUCING sugars. The stem tells us the positive result is due to a NON-glucose reducing substance, so glucose itself is not the culprit. In a milk-fed infant, the reducing sugar that floods the system is galactose (from lactose). This already tilts us toward a disorder of galactose metabolism.
Step 2: Tie the timing of symptoms to the feed.
The baby vomits AFTER FEEDING on milk. A condition that becomes symptomatic the moment milk (lactose → galactose) is introduced must sit on the galactose pathway and must be severe enough to cause toxicity early. That severity points to classic galactosemia.
Step 3: Localise the enzyme block.
Classic galactosemia is caused by deficiency of galactose-1-phosphate uridyltransferase (GALT). The block lets toxic galactose-1-phosphate accumulate (damaging liver, kidney, brain → vomiting, jaundice, hepatomegaly), while free galactose spills into blood and urine, giving the positive non-glucose Benedict's reaction.
Step 4: Rule out the alternatives.
• Hereditary fructose intolerance (aldolase B) → triggered by FRUCTOSE/sucrose, so symptoms appear after weaning onto fruits/sweets, not with early milk feeds.
• G6PD deficiency → causes oxidative haemolysis after triggers, not post-feed vomiting, and does not give a non-glucose reducing sugar.
• Galactokinase deficiency → also a galactosemia and Benedict-positive, but it is the milder variant whose dominant problem is cataracts, lacking the severe acute vomiting/hepatic picture seen here.
Final answer: The severe milk-triggered presentation with a non-glucose reducing sugar is Galactosemia due to GAL-1-P uridyl transferase enzyme deficiency (Option 1).