The most likely diagnosis is autosomal dominant polycystic kidney disease (ADPKD). The hallmark of ADPKD is large kidneys with multiple kidney cysts, and patients may have resulting chronic, mild abdominal discomfort; in some cases, palpable abdominal masses occur, as in this patient. Patients with ADPKD may also present acutely with severe pain and hematuria resulting from bleeding of a cyst, as seen in this patient. ADPKD is the most common inherited kidney disorder, occurring in 1 of 400 to 1 of 1000 live births. Although transmitted in an autosomal dominant manner, a negative family history does not necessarily exclude ADPKD. Approximately 15% of patients with ADPKD have spontaneous mutations that result in the disease. Alternatively, one of the patient's parents may have a less severe phenotype without clinical manifestations.

Renal cell carcinoma does not occur with greater frequency in patients with ADPKD than in the general population and does not present with bilateral abdominal masses.

Renal vein thrombosis may present with acute-onset flank pain and macroscopic hematuria and may show enlargement of the involved kidney. However, renal vein thrombosis does not result in bilateral abdominal masses and is more commonly seen in hypercoagulable states, such as the nephrotic syndrome or the antiphospholipid antibody syndrome. This patient has no evidence of hypercoagulability.

Gross hematuria often occurs in patients with urinary tract infection. However, this patient has no accompanying urinary symptoms, and the leukocytes in her urine are likely the result of gross bleeding into the urinary tract. Additionally, urinary tract infection would not explain the abdominal masses seen in this patient.