Are you sure it's hypoglycemia? I only ask because I used to have it and eating protein/more protein never affected it. It's a blood sugar problem. Also, for myself, that's not how I would describe it. I get painfully hungry, start shaking, feel weak, and nauseated. Eating anything helps get rid of it. It always returns if I eat too much refined sugar in the morning.
If you don't feel particularly full at breakfast with 3 eggs, that doesn't sound like you are eating enough food, but I guess that depends on how you space out the meals for the rest of your day, and if you are fairly short.