• Infant with recurring infections, eczema and thrombocytopenia, most consistent with Wiskott-Aldrich syndrome
• Adenosine deaminase deficiency = Severe combined immunodeficiency –> Failure to thrive, recurrent infections with all types of organisms
• Ataxia telangiectasia –> Cerebellar defects (ataxia), IgA deficiency (anaphylactic blood transfusion reactions, sinopulmonary infections), spider angiomas
• DiGeorge syndrome –> CATCH-22 (Cardiac defects, Abnormal faces, Thymic aplasia, Cleft lip/palate, Hypocalcemia (due to lack of parathyroid glands)
• Hyper-IgE –> Cold staph abscesses (contrast with abscesses without pus seen in leukocyte adhesion defect), coarse faces, retained primary teeth, easy bone fractures
• Infant HIV –> Chronic diarrhea + failure to thrive + opportunistic infections (thrush, etc.)
• X-linked agammaglobulinemia –> Patient with history of uncles who die of infection who develops recurrent bacterial (due to lack of IgG) and mucosal (due to lack of IgA) infections found to have decreased levels of all immunoglobulins

https://step-prep.org/tutoring/

The symptoms of Wiskott-Aldrich syndrome may be remembered with the mnemonic "WATER":

W: Wiskott

A: Aldrich

T: Thrombocytopenia

E: Eczema

R: Recurrent (pyogenic) infections

UptoDate says IgG and IgM are notably low to normal and IgA and IgE are supposed to be high. So not sure why the labs are the way they are in this question.