Diabetic Ketoacidosis (DKA): Given the patient's elevated glucose level (236 mg/dL), abdominal pain, diaphoresis, and elevated white blood cell count, DKA is the most likely diagnosis. The family history of diabetes further supports this diagnosis, as it suggests a predisposition to diabetic conditions.

Hyperglycemic Hyperosmolar Nonketotic Syndrome (HHNS): Although less likely than DKA due to the absence of ketosis indicators, HHNS could still be a consideration given the patient's hyperglycemia and potential for dehydration.
Sepsis: The elevated white blood cell count (16.3 x 10^9/L) and abdominal pain could indicate an infectious process, possibly leading to sepsis, especially if the patient has a compromised immune system due to uncontrolled diabetes.
Acute Pancreatitis: Abdominal pain and elevated glucose could also suggest acute pancreatitis, particularly if there's a history of gallstones, hypertriglyceridemia, or alcohol use.

Appendicitis: Although less likely given the context, appendicitis is a condition that could present with abdominal pain and an elevated white blood cell count. Missing this diagnosis could lead to severe consequences, including perforation and peritonitis.
Ectopic Pregnancy: In a female patient of childbearing age presenting with abdominal pain, ectopic pregnancy must be considered, especially if there's a possibility of pregnancy.
Ovarian Torsion: Another gynecological emergency that could present with acute abdominal pain and requires prompt diagnosis to preserve ovarian function.

Pheochromocytoma: A rare tumor of the adrenal gland that could cause episodes of hypertension, diaphoresis, and abdominal pain, though it would not directly explain the hyperglycemia.
Fulminant Type 1 Diabetes: Although the patient's age and family history of diabetes might suggest type 2 diabetes, fulminant type 1 diabetes is a rare condition that could present with rapid onset of hyperglycemia and ketoacidosis.

The treatment plan would primarily focus on the most likely diagnosis, DKA, with adjustments based on further diagnostic findings:

Fluid Replacement: Aggressive fluid resuscitation to correct dehydration.
Insulin Therapy: Administration of insulin to lower blood glucose levels.
Electrolyte Replacement: Particularly potassium, to prevent hypokalemia.
Monitoring: Close monitoring of glucose levels, electrolytes, and fluid status.
Infection Screening: Given the elevated white blood cell count, screening for potential infections.
Imaging: If abdominal pain persists or worsens, consider abdominal imaging to rule out other causes like appendicitis or pancreatitis.

Follow-up would involve:

Regular monitoring of blood glucose levels and adjustment of diabetes management plan.
Evaluation of renal function given the family history of chronic kidney disease.
Screening for complications of diabetes and management of associated risk factors.
Patient education on recognizing and managing DKA, as well as long-term diabetes management.