If you could, move to a sunny state, it's easier to be on such a diet and full of energy if you are in warmer climate. Once during winter I did keto, daily cold shower, daily HIIT, 3-4x strength training/week and then I lost all energy and got sick for a month. I did the same in summer and it was all great.
Did you take into account your extra energy requirements in the winter? Your body has to keep you warm and this uses energy. It would be interesting to have an app or wearable that could help you keep up with intake based off of your environment (e.g. yesterday you walked n+10 miles and it was cold, you should eat more today than normal).
No, I didn't at that time. An app like one you mention would have to observe you first and see which foods give you what amount of energy, as your body is cherry-picking compatible food to some extent and burning rate is highly individual, probably even depending on your gut bacteria and how they pre-process your food. What works for one person won't for another :(
To get your energy back, you have to do little or no calorie restriction, 500 calorie deficit tops. I'd say start first with no calorie deficit (even if it's hard on a fat diet because you feel full) and see if that improves it.
For the headaches and the rest, you have to up your electrolytes: sodium, potassium and magnessium. Your body on ketosis will excrete much more of them than usual. Occasionally I get a pretty bad headache that goes away with 1/2 a teaspoon of salt, sometimes even more.
