Spot diagnosis: thick shiny membrane at birth = collodion baby = lamellar ichthyosis.
Run the options down. X-linked ichthyosis appears in male infants over the first weeks with large, dirty-brown polygonal scales (steroid sulfatase deficiency) but does not present as a membrane-wrapped newborn. Ichthyosis vulgaris, though the most common ichthyosis overall, declares itself later with fine white scales on extensor surfaces and accentuated palmar creases, never as a collodion membrane. Ichthyosis acquisita is, as the name says, acquired, seen in adults as a paraneoplastic or drug-related sign, so it is impossible in a neonate.
Lamellar ichthyosis is the autosomal recessive congenital ichthyosis whose hallmark newborn picture is exactly the collodion membrane that later sheds to reveal large plate-like scales. The barrier defect impairs water retention, giving the dry scaly skin and the encasing membrane.
Ref: Arvind Arora Skin 6e.