Do I have an eating problem?

You're not getting enough nutrients throughout the day. The reason why people binge eat is not really because they're hungry, but because the body hasn't gotten the sufficient amount of nutrients it needs, so it sends signals to the brain that it needs more food to try and make up for the calorie and nutrient deficit. It depends on what you're eating for breakfast and lunch that would say better how you can improve. But I recommend eating more carbs throughout the day. They'll give you energy and keep you full. Carbs like fruits, veggies, grains. Oatmeal for breakfast would be great. Apples and bananas and other fruits throughout the day would help you better also. As for the headaches I'm not sure either but you could be not drinking enough water/ again eating enough food. Remember you should always be peeing clear and pooping 2-3 times a day!

Binge eating is likely the result of low blood sugar from not eating for so long, and headaches are likely the result of either not enough water or also low blood sugar. To solve low blood sugar, eat small meals more frequently, even if its only a few bites, protein, whole grain breads, fruit, you know, the stuff mother nature gave us for food. Stay away from processed foods, artificial sweeteners, etc, those are just bad news for your body.

So in a nutshell I guess what I'm saying is "Drink water, Eat food, make it mostly vegetables and fruit. The end."

That's possible. Take a copy of your post to someone like a therapist to discuss ways to improve. You'd be surprised how helpful it can be.