Hi, I don't know if I have answers, but I do think it's normal. When I first got sober I felt lethargic and foggy-brained and physically lazy/ like a hangover on and off for months-- sometimes stronger than others. Honestly I was quite unproductive, with little to no motivation, and would replace my addiction to alcohol with an addiction to sugar/fast foods/ice cream and TV watching. :-/
This time around (I'm only at 12 days and last time I had over 6 months), I have not really had that effect so far. I actually had some other health problems in between sobriety stints but right now I am trying to stay active and energetic, to get things done and be productive, to eat better, and soon I want to start working out again. However this time around I seem to feel more mentally off/depressed, or just resigned to dealing with this alcohol problem forever, which bums me out.
I think that our bodies and minds have to even out and have a lot to deal with after we stop drinking. I have heard that the effects (called PAWS) can last for 6 months to a year or longer, sometimes 2 years or more. But at least we're on the right track and we are not increasing our problems by drinking! Best wishes to you.