I hope I don't come across as rude, but with all due respect, I'm not sure if it's the lack of caffeine your body is reacting to. I think it's the lack of sugar.
Yes, Coke does contain some caffeine but you'd be surprised... there's actually not that much caffeine in it. What it is full of though, is sugar, and lots of it.
I say this because I also drink a lot of a drink that I should not be having. I love iced coffee. The iced coffee I drink, next to Coke, is probably one the worst drinks your body can have. It's 600mL of milk that essentially has a tiny bit of coffee in it and loads of sugar. It tastes amazing but it's not good for you at all.
Earlier this year I went on a diet and I was required to cut out sugar, this meant no iced coffee. The first week was hell. I experienced massive head aches. I became easily agitated and stressed. I didn't sleep well for the first few days and I felt so tired and drained. Eventually, I started to have iced coffee only once a week, instead of almost every day. When I craved something "sweet", I would drink either Coke Zero or Diet Coke. No sugar. No calories. Yeah, it's got other crap in it that's just as bad, if not worse, but since I was only concerned about my weight at the time, it was okay.
So apart from diet soft drinks, one thing that also helped me was eating. The diet required me to eat a lot of food (despite the fact it was a weight loss diet). I was eating 3,500 calories a day. Oats, almond milk, protein powder, rice, green vegetables, lots of chicken breast. It was actually kinda hard to eat so much food and man, I love to eat, but I found as I ate, I often stayed full and I didn't really think about wanting sugar. That being said, it doesn't stop the cravings, but it helps.
Sugar is an addictive substance. So is caffeine. They're like drugs. Like I said before though, drinks like Coke and iced coffee don't actually have that much caffeine in it. It's the sugar that's making us so drawn to it. It's also because of the sugar that makes our bodies freak out when we don't have it. When we consume so much sugar on a regular basis, our bodies dig it, it enjoys it, our brains are almost "rewarded" for having it. When we take sugar out of our diet, especially if we do so cold turkey, then our bodies and brains pretty much freak out - "WHERE THE FUCK IS MY SUGAR?!" it'll scream, as we start experiencing symptoms like head aches, agitation, insomnia, fatigue and so forth. The withdrawals suck.
Maybe you haven't "quit" sugar, per say... maybe there is still sugar in your diet? Just keep in mind, Coke has lots of sugar. You also mentioned that ever since you were younger, you've been drinking 2 liters of Coke per day. A 2 liter bottle of Coke contains roughly 216 of sugar. That's a quarter of a kilogram. That's A LOT of sugar, especially when you've been having it for a long period of your life, every day. When you give up that much sugar in one go, even if you are still eating some foods with sugar in it, of course your body is going to freak out and give you grief.
I think it's great that you're quitting Coke, or at least giving it a break. It'll do you wonders. The first week or two is going to suck, but you will be better off for it. In all honesty, if you need some help and you're craving something "sweet", I'd suggest drinking either Coke Zero or diet Coke - in smaller amounts (e.g. opt for a 600mL bottle instead of 2 liters).
TL;DR - I'm pretty sure it's not the lack of caffeine your body is freaking out to, it's the lack of sugar. 2L of Coke a day is a lot of sugar. Going cold turkey is going to freak your body out. Keep it up, drink diet soft drinks and smaller amounts of it to help you cope.
