Yes!
But not necessarily in the way you think.
If you are dieting migraine can be a nightmare and your diet does sound like a migraine in the making for me.
Hunger is a massive migraine trigger so dieting has to be done very carefully. If you are getting a low blood sugar because of your diet, your body will not like that at all.
Equally migraine likes regularity - regular meals, getting up at the same time, going to bed at the same time, having loads to drink. If your diet has changed this, again, recipe for disaster. If I don't have lunch within a 30 minute window every day, I start feeling really ill and too late there will be a migraine.
Finally you have cut out a lot of food groups - fats, sugars AND carbs. For lots of people migraine seems to be linked to activity of the vagus nerve. So changing diet can be a good thing to help control migraine but you have to do it carefully to avoid all the hunger triggers.
Your vagus nerve basically controls your appetite. It is what makes you hungry and tells you that you need to eat a load of carbs and sugars even though you might, in my case already be fat It's why low carb, low sugar diets are so in for helping diabetes, if you cut them down, your appetite reduces as well as losing loads of weight. So much less feeling hungry (good because less migraine) and less eating of fattening foods.
So a good migraine diet would be cutting out sugar, low carb, healthy oils and fats, wholegrains, high fibre, loads of veg - still making sure you didn't get too hungry between meals but slow weight loss 2 pounds a week. A bit like the healthy Mediterranean diet everyone is recommended!