No I've found just the opposite as have a number of other people, and there was a thread about this last year. I suffered chronic migraines since my early teens with various, including food related, triggers. I suffer very few now (mainly stress and weather related) and the food related ones have more or less completely stopped since I started LCHF over three years ago. I can actually enjoy in moderation some of the foods such as dark chocolate and blue cheese that I've previously had to avoid.
I don't seriously fast, but if I remember correctly Kevin Potts who started that thread, did. So it may depend on what you're eating or the ingredients in any shakes you might be using - I'm pretty sure that certain additives in my pre-LCHF diet also did me in !
It's also worth doing a search too (here and Google) on low carb/Atkins/keto "flu" as cutting right down on carbs after eating a high carb diet can cause withdrawal symptoms (including headaches) for a while. Drinking plenty of fluids and making sure that you are getting enough minerals (salt, magnesium, potassium) as you will probably be weeing more and your kidneys will be flushing more of these out.
Robbity