Nephrolithiasis (Kidney Stones): Given the abdominal pain and singular kidney, kidney stones are a plausible cause. The elevated calcium level could contribute to stone formation. However, the elevated eosinophils are not typically associated with kidney stones, making this diagnosis less straightforward.

Urinary Tract Infection (UTI): Although UTIs are common in children, the presence of a singular kidney and elevated eosinophils might suggest a more complex infection or an allergic reaction. The elevated potassium could be due to renal impairment.
Acute Kidney Injury (AKI): The singular kidney and abnormal electrolyte levels (elevated potassium) could indicate AKI, possibly due to an obstructive cause like a kidney stone or a non-obstructive cause such as infection or medication.
Allergic Interstitial Nephritis: This condition, often caused by medications or infections, can lead to elevated eosinophils and renal dysfunction, manifesting as abdominal pain and electrolyte imbalances.

Hyperparathyroidism: Although rare in children, primary hyperparathyroidism could explain the elevated calcium level. It's crucial to consider this diagnosis due to its potential for significant morbidity if left untreated.
Sepsis: In the context of abdominal pain and a singular kidney, sepsis of renal origin (e.g., pyelonephritis) must be considered, especially if there are signs of infection or systemic illness. The elevated potassium could indicate renal dysfunction.
Obstructive Uropathy: Given the singular kidney, any obstruction (e.g., due to a stone) could lead to severe consequences, including loss of the only functioning kidney.

Lymphoma: Although rare, lymphoma can cause abdominal pain, renal impairment, and electrolyte disturbances. The elevated eosinophils could be part of a paraneoplastic syndrome.
Eosinophilic Granulomatosis with Polyangiitis (Churg-Strauss Syndrome): This rare autoimmune condition can affect the kidneys and is characterized by elevated eosinophils. However, it is exceedingly rare in children.
Tubulointerstitial Nephritis and Uveitis Syndrome (TINU): A rare condition that can cause renal dysfunction and is associated with elevated eosinophils, though it is more commonly diagnosed in adolescent females.

Imaging: Ultrasound of the abdomen to evaluate the singular kidney for stones, obstruction, or other abnormalities.
Laboratory Tests: Complete Blood Count (CBC) with differential, blood urea nitrogen (BUN), creatinine, electrolyte panel, urinalysis, and urine culture.
Eosinophilic Evaluation: Consider testing for parasitic infections or allergic causes of eosinophilia.
Renal Function Tests: To assess the singular kidney's function and guide further management.
Parathyroid Hormone (PTH) Level: To evaluate for hyperparathyroidism, especially with elevated calcium levels.