Keto is the only thing that fixes my depression-like state. I discovered it doing short-term fasts and then learned about Keto.
I tested it multiple times. Once I get off Keto I feel much worse within 2 weeks and after around 1 month I am at the total bottom again. Then go back to Keto, 2-3 days of suffering Keto Flu and I'm happy to live again.
Your body is switching to ketosis. You can read about it a lot and it's literally called keto-flu by the keto diet community :) If you want to ease the transition, you should first get into ketosis, but not fasting yet(so still eating but not carbs), and after ket-flu is gone then try fasting.
From my experience all that comes from shock to the body. You are simply not used to it. It gets better over repeated attempts.
Also for the headache - do you still drink caffeine? Brutal headaches usually come from caffeine withdrawal(if you normally drink it but stop during fasting). If that is the case you need first to drop caffeine slowly lowering your daily dosage so the headaches won't happen.