The headaches and brain fog are symptoms of low sodium. Are you supplementing sodium?

In my experience (I was keto for 1.5 years until I got to goal) and from listening to all the members here and in other forums there are many people who have a more noticeable hormone shift. Hormones run everything basically and any big diet change can potentially impact that in a big way. Also, weight loss mobilizes stored estrogen so many report a 3 or 4 months disruption to their cycles (and also lack of skin clearness and the cranky and BO and greasy hair) that eventually resolves positively. And since intake and digestion and blood sugar regulation are also hormone driven, that surge when having to deal with those processes sounds like it might impact some. I experienced the hot flash some on keto, particularly if I was doing IF and my fasting window was long. After I finally broke my fast, I would indeed feel a flush. Don't get me started on my level of sweatiness for awhile.

All that to say that it's hormones, and it will hopefully die down after a few months once everything sorts itself out. YMMV.