Your story is certainly interesting and somewhat compelling. Please see Classification and Diagnosis of Diabetes.
At present, based on what you’ve written, I do not think your son has diabetes mellitus but, again, the story is atypical. While you have double-checked your meter and the codes, and the control solution, etc, have you double-checked your blood checking technique by assuring that his finger is CLEAN and DRY before getting the blood droplet?
The test you referred to as the “hemoglobin test” was probably really the “Hemoglobin A1c” test, which can give an estimate of what the glucose levels have been over the past several, several weeks. So, this test can be normal even in someone with diabetes (very recent onset or in fabulous control); it is NOT used to establish a diagnosis of diabetes.
Is there a family history of diabetes, especially type 1 diabetes, or other autoimmune disease? If diabetes were really suspected, this might be one of those rarer time that a properly performed Oral Glucose Tolerance Test (OGTT) might be warranted. Pancreatic antibody testing for type 1 diabetes might be something I would hold off.
Typically, in diabetes, there would not be glucose in the urine until the blood glucose was maintained above 180 mg/dL [10.0 mmol/L] for a bit.
Many, many other conditions can lead to increased urination and increased thirst. Substantially increased thirst associated with NON-concentrated urine as you allude to brings to mind a different hormonal condition, confusingly called “diabetes insipidus” which has NOTHING to do with glucose. What’s your son doing at night? Is he awakening to drink and/or urinate then, too? Is he drinking from “odd” sources? Is he wetting the bed? Is he preferring particular fluids to drink?
Please continue to meet with your pediatrician who may want to refer you to or consult with a pediatric endocrinologist when the initial screen studies are back.
Please let us know what you learn.
DS