I had headaches the first week I went on low carbs. I think it was part of the carbohydrate withdrawal symptoms. I didn't give up coffee and I never drank soda, so it wasn't that. I think it was the lack of sugar.
Just take a couple of advil and lots of water. Your symptoms should go away soon. How long have you been dieting? If you cheat and go back on low carbs or no sugar, the symptoms will probably return and you'll have to go through it again.
Keep at it. It's worth it!