Zinc Deficiency: Given the boy's slow-healing tendinosis, history of allergies, and frequent illnesses, zinc deficiency is a plausible diagnosis. Zinc plays a crucial role in immune function, wound healing, and protein synthesis, which could explain the boy's symptoms. The low albumin level (4.3) may also indicate malnutrition or zinc deficiency.

Vitamin D Deficiency: This condition can lead to impaired immune function, frequent illnesses, and musculoskeletal issues, including tendinosis. The boy's phosphorus level is slightly elevated, which could be related to vitamin D deficiency.
Celiac Disease: This autoimmune disorder can cause malabsorption of essential nutrients, leading to frequent illnesses, slow healing, and musculoskeletal issues. The boy's low albumin level and history of allergies may be indicative of celiac disease.
Immunodeficiency: The boy's frequent illnesses and slow-healing tendinosis may suggest an underlying immunodeficiency, such as common variable immunodeficiency (CVID) or selective IgA deficiency.

HIV Infection: Although less likely, HIV infection can cause immunodeficiency, frequent illnesses, and musculoskeletal issues. It is essential to consider this diagnosis to prevent delayed diagnosis and treatment.
Leukemia or Lymphoma: These cancers can cause frequent illnesses, musculoskeletal issues, and abnormal blood cell counts. Although the boy's blood cell counts are not significantly abnormal, it is crucial to rule out these diagnoses.

Ehlers-Danlos Syndrome: This genetic disorder can cause musculoskeletal issues, including tendinosis, and may be associated with immune system dysfunction.
Chronic Granulomatous Disease: This rare genetic disorder can cause recurrent infections and musculoskeletal issues due to impaired immune function.
Autoimmune Lymphoproliferative Syndrome (ALPS): This rare disorder can cause immunodeficiency, frequent illnesses, and musculoskeletal issues due to abnormal lymphocyte proliferation.