Do you eat a lot of sugar? I used to have pastries or cereal and sugar with my coffee at breakfast and sometimes throughout the day. Like for you, a skipped meal or snack meant headaches. I've since weaned off sugar and I can easily go many hours without eating or snacking. I no longer eat breakfast.
I suspect that the blood sugar spikes were addictive, i.e. my body desensitized and needed me to frequently consume sugar to keep my blood sugar level high.
Try gradually reducing the amount of sugar that you consume, and/or the total amount that you eat at breakfast, as well as the frequency of your snacks throughout the day. Eventually you should be able to do fine on two good meals a day and nothing else.