I have a similar situation -- I was feeling terrible and run-down all the time, like I could never get enough rest. I'd get mid-afternoon headaches everyday, and I was being irritable even with the people closest to me. I went to a Dr to figure it out, and of course she just wanted to test for low iron, thyroid problems, etc... I asked her if, out of curiosity, I could get a fasting blood sugar test done since I have a family history of diabetes and was beginning to think my body didn't respond normally to what I eat....
And lo and behold, the only thing that came back abnormal was the blood sugar. Now I know I'm a reactive hypoglycemic and have seen a dietician about what I ought to do.
Seriously, the best thing to do is NOT to skip breakfast, and not to skip anything at all. I eat every two and a half hours, and have a restricted carb intake. Actually, I'm on a diabetic diet plan with more strictly-restricted carb allowances. At first it was a pain, but I've been on it a week and I now realize how much better it makes me feel, especially in getting me through long lectures in the afternoon! It also encourages me to eat way more fruit and veggie snacks than before.... I used to just snack on whatever was around -- crackers, chips, cookies, etc.
I'm also learning to avoid sugar and refined white flour, but THAT's a hard undertaking. I'm a total sugar addict, and I'm really trying to stay away from it... It's just not good for me, it makes me feel awful. I can imagine that you feel this way too when you eat one of these trigger foods.
I would recommend trying to see a dietician..... she'd really help with listening to your symptoms and trying to identify what it is that's making you so tired after eating. There may just be some element that your body doesn't like.
I used to think that if I just ate when I began to feel tired I'd be ok -- that's the wrong way to do it, it's too late then! (And then there's the 10lbs weight gain...) I found that the structure given to me by the dietician has seriously helped me. She can help with weight loss too, if you note that it is a concern.
Good luck on your journey. I hope all goes well, keep us posted!