There is no reason to cut carbs from a diet. Calories make you gain weight , not any specific source.
Eating no carbs means you're consuming an unhealthy amount of fats and proteins. (Very high protein intake is hard on the kidneys.)
When you deplete your glycogen stores, you also lose the water that is stored with it. Weight loss for this reason is generally in the 3-5 lbs range. You have not lost real weight.
Depression can be a result of low blood sugar.
Return carbs to your diet (at least 40% of calories) and focus on complex carbs.
Carbs have been demonized for the sake of selling diet plans and books.
"To give anything less than your best is to sacrifice the Gift."