Hi , noted your concern. Looking at your family history of diabetes, it's likely that you may develop diabetes if your lifestyle is not good. Hba1c 6  and abnormal fasting sugars indicate that your sugars are in prediabetes range. The best thing is , this is the stage from where you CAN PREVENT future type 2 Diabetes by very careful diet modifications and optimization of weight, with good exercise.

Hba1c betwwen 5.7 and 6.4 is prediabetes and since you have a strong family history of diabetes your tendency to develop diabetes is very high.lifestyle modifications like brisk walk for 45 minutes per day for 5 days a week and reducing carbohydrate and sugar intake will help.

Your HBA1C shows pre diabetes stage. You are having impaired fasting glucose levels. So please focus on weight reduction and Diet counselling. Repeat test after three months. Also check TSH levels.