I cut out the carbs at the same time I quit drinking. I lost 30 lbs in 4 months and since then (I've been sober 8 months) I've kept it off. I also quit smoking when I was 4 months sober and I'm still smoke free.
You know your own body and what you can or can't handle. It's good that you're aiming to be healthy, but don't be too hard on yourself right now. If you need to rest, then do so. If you need a pick-me-up treat, then have one. Nobody can be perfect 100% of the time.