If you use your glucometer to see what happens after you have eaten, you can easily see if you are going hypo.
I would start a food diary, record your pre meal reading, your hour reading and two hours reading, then again at three and four hours, if you hypo, treat it asap.
If you find you are, I would definitely return to your GP and ask for a referral to a specialist endocrinologist who has experience with hypoglycaemic conditions.
I would also recommend reading the RH forum and seeing if anything is similar.
Are you on any meds at all?
What symptoms are you getting?
My fasting levels are always in normal range.
My Hba1c is always in normal range.
I only go hypo when I have food!
But it only happens if I have carbs or sugars!
Best wishes.