Frequent and long-term exposure to hyperglycemia (i.e., high blood glucose) increases the risk of chronic complications such as neuropathy, nephropathy, and cardiovascular disease. Current technologies like continuous subcutaneous insulin infusion (CSII) and continuous glucose monitoring (CGM) primarily model specific aspects of glycemic control-like hypoglycemia prediction or insulin delivery. Similarly, most digital twin approaches in diabetes management simulate only physiological processes. These systems lack the ability to offer alternative treatment scenarios that support proactive behavioral interventions. To address this, we propose GlyTwin, a novel digital twin framework that uses counterfactual explanations to simulate optimal treatments for glucose regulation. Our approach helps patients and caregivers modify behaviors like carbohydrate intake and insulin dosing to avoid abnormal glucose events. GlyTwin generates behavioral treatment suggestions that proactively prevent hyperglycemia by recommending small adjustments to daily choices, reducing both frequency and duration of these events. Additionally, it incorporates stakeholder preferences into the intervention design, making recommendations patient-centric and tailored. We evaluate GlyTwin on AZT1D, a newly constructed dataset with longitudinal data from 21 type 1 diabetes (T1D) patients on automated insulin delivery systems over 26 days. Results show GlyTwin outperforms state-of-the-art counterfactual methods, generating 76.6% valid and 86% effective interventions. These findings demonstrate the promise of counterfactual-driven digital twins in delivering personalized healthcare.