Is it possible to have hypoglycemia when in great shape and eat right?

I have been eating right with a plate of 1/2 vegetables, 1/4 lean meat, and 1/4 grain each meal for lunch and dinner and simple egg/small bowl sugar-free cereal w/milk, etc. I am also in the greatest shape of my life: I am gaining muscle and strength on daily basis but still no endurance at all! I feel like no matter how much I eat it isn't enough and have problems no matter what I eat keeping my blood sugar in the 80s and can only reach 90s if eat really bad stuff like pizza, ice cream, sugar, etc. (always in low 70s, and dips into 60s/50s) . I only feel I have energy when in the 90s at that high, when I am at 80 I'm ok but only moderate energy. At 70s feel weak and can't think well and at 60s and 50s I feel confused, weak, disoriented, shake, or have heart flutters, etc. Everyone seems to say that hypoglycemia can be cured by taking out sugar but I have always had hypo episodes since teens and ate pretty well even then. This last week I started eating sugar but only because nothing else seems to make me feel ok. What is wrong with me? Taking out sugar doesn't help me at all!