In my experience, headaches from cutting out carbs are almost always because your body is retaining less water and you're running low on water/electrolytes. Add some salt, zinc, magnesium and potassium to your diet.

When I do extended fasts (1-5 days), I'll literally grind up cal-mag-zinc pills, add salt, and dilute them in warm water and drink them. It tastes awful, and there's products out there that work better, but it feels great once your body absorbs it.