Diabetic Neuropathy: This is the most likely diagnosis given the patient's history of uncontrolled type 2 diabetes mellitus (T2DM) and complaint of bilateral hand numbness. Diabetic neuropathy is a common complication of diabetes, resulting from damage to the peripheral nerves due to high blood sugar levels over time.

Hypothyroidism: Often associated with diabetes, hypothyroidism can cause numbness or tingling in the hands and feet. The connection between thyroid disorders and diabetes, along with the symptom presentation, makes this a plausible diagnosis.
Vitamin B12 Deficiency: This deficiency can cause neuropathy, leading to numbness or tingling in the hands and feet. It's particularly relevant in patients with diabetes, as metformin, a common diabetes medication, can interfere with B12 absorption.
Carpal Tunnel Syndrome: Although more commonly associated with unilateral symptoms, bilateral carpal tunnel syndrome could cause hand numbness. It's less directly related to diabetes but is a common condition that could coexist.

Acute Stroke or Transient Ischemic Attack (TIA): Although less likely given the duration and nature of the symptoms, it's crucial not to miss a stroke or TIA, as these are medical emergencies requiring immediate intervention.
Multiple Myeloma: A rare condition, but one that can cause neuropathy. Given the potential severity of this diagnosis, it's essential to consider it, especially if other risk factors are present.

Amyloidosis: A group of diseases that can cause neuropathy among other symptoms. It's rare but could be considered if other diagnoses are ruled out and the patient has specific risk factors or additional symptoms suggestive of amyloidosis.
Sjögren's Syndrome: An autoimmune disorder that can cause neuropathy. It's less common but should be considered if the patient has other symptoms such as dry eyes or mouth, or if they have a history of autoimmune diseases.