Final answer:
The condition with increased risk of infection, eczema, thrombocytopenia, and small platelets is Wiskott-Aldrich syndrome (WAS), not Systemic lupus erythematosus (SLE) which is an autoimmune disease affecting various organs.
Step-by-step explanation:
The condition characterized by increased susceptibility to infection, eczema, thrombocytopenia, and the presence of unusually small platelets in the patient's blood is Wiskott-Aldrich syndrome (WAS). Systemic lupus erythematosus (SLE) is an autoimmune disease characterized by a wide range of symptoms due to autoimmunity to the individual's own DNA and/or proteins. While SLE involves various organs and systems in the body, it is not typically associated with thrombocytopenia and small platelets, which are characteristic of WAS.