Those symptoms are consistent with what I have seen when folks are transitioning to a ketogenic diet. We’re not big on the keto diet here at UA. Not because it does not work. It will make you very fat adapted over time but it is very hard to maintain and if you fall off the diet then you have to go through this very unpleasant transition period again….and again….and again. It can also be awkward to to be that person who can’t eat certain thing when in a social setting. And it is not necessary to accomplish fat adaptation.
We advocate; in the many articles on this site and in the recent podcast I did with Rebecca, a more tempered approach. Reduced carb intake coupled with training in Z1-2 has proven in hundreds of athletes we’ve worked with to cause good fat adaptation without the severe side effect that you are experiencing.
This experiment you have been conducting seems to show that this is not working well for you. I would suggest a more moderate approach like we recommend. Do not make major shifts in diet or training. Be very gradual about introducing these things and you body will adapt but it if you hit with a big hammer it will rebel.