when you first start eating low-carb, your body begins by using up the store of glycogen (stored carbohydrate) that it has packed into your muscles and liver for easy access. Each molecule of glycogen is packed with four molecules of water. So when that glycogen is released so your body can use it as fuel, that water is released, too.
That's why low-carb can show such drastic initial weight loss. It slows down after a few weeks, to a slower loss but a loss more specifically of fat.
has one of the best explanations of this I've found online.
The "icky" feeling is probably carb flu, as you suggest. If you're drinking water, I doubt you're actually dehydrated.
Carb flu will disappear as your body gets used to using ketones (from fat) for its main fuel rather than glycogen (from carbs). Right now it's switching gears, and that takes some time.
If it gets too bad, you may want to eat a few more carbs (depending on your plan). Some people can "ease" into lower carb by eating fewer than 100 grams of carbs a day for a couple weeks, then lowering it even more. Others prefer the quicker route of dropping to very-low-carb (20 grams/day or fewer, like Atkins "induction"), knowing they will have "carb flu" until their body adjusts, because they know it will only take a few days.