Bilirubin given in question is very high; Bilirubin binds to Albumin in blood, so when any drug displaces bilirubin from albumin, it can lead to increased free bilirubin. Cotrimoxazole is a combination of trimethoprim and sulfamethoxazole (a sulfonamide). Sulfonamides (acidic drugs) can displace bilirubin from albumin resulting in excessive free bilirubin. This can cross blood brain barrier in newborn babies which can cause Kernicterus; hence avoided in pregnancy.
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