50 eggs a week--whoa, cool hand Luke!
Seriously, not everyone can tolerate ZC/low carb. If it was just "induction flu", you would probably feel better by now.
Consider adding more veggies and starchy tubers back into your diet until you feel better.
As far as being a "hard gainer", adding some carbs may help you there as well. Insulin is an anabolic hormone. In fact, one of the most popular mass gaining diets is "GOMAD" (gallon of milk a day), which is a high insulin strategy (and definitely not paleo).
On the other hand, once you dial in your optimal carb intake for health and energy level, you may want to go with more of a Leangains muscle-building approach, which ideally does not involve gaining fat along with the muscle.
Restore your health and energy first, then move on to muscle gains.
(Note: I'm not advocating GOMAD, just using it to illustrate the anabolic property of insulin.)