An A1c is a measure of how much glucose is stuck to your red blood cells. Its based on red blood cells living qn average of 90 days. If your red blood cells have a shorter life then your A1c will be abnormally low. Also the A1c is an AVERAGE so if your BG goes high after eating and then lower the rest of the time then it AVERAGES out to a normal ish number.
Ask for a GTT test "glucose tolerance test" and make sure they test your BG every 15 minutes for 3 hours. Not just at 2 hours. The GTT with testing will give a lot more info on how well your body regulates your BG.
what was your hba1c level?
According to some experts, truly normal Hba1c level is about 4.3 - 4.6 which gives an average blood sugar of about 75 - 85, and not higher than 5.0 (average blood sugar about 100). However, the labs will typically say that normal results are up to 5.7 (average blood sugar about 125).
Blood sugars vary from fasting levels thought to post eating. So a 'normal' hba1c can actually reflect normal fasting levels and abnormal post eating levels, or vice versa. Hba1c alone is not adequate to rule out problems. Thus, even a 'high normal' hba1c should trigger further evaluation.
Have you tried eating low carb (ie. carbs come mostly from non-starchy vegetables, higher healthy fats and proteins)? This may help and you won't starve.
Sounds like you could be describing early type 2 diabetes.
You are having early warning and can learn about this and take measures to address it and prevent progression.