Hypoglycemia in morning

Patient: I have been checking my blood glucose in the morning lately and I have been getting values around 2.5. Is it ok for my glucose levels to be so low every morning? I have asked my doctor previously why I frequently faint due to low blood sugar and all he said was to eat more often. Diabetes runs in my family, should I go back to my doctor with the morning values? Thanks for your help

Doctor: