Fad diets don't necessarily supply us with the nutrients we need. They are short-term fixes for a long-term problem. Have no idea what's happening with you, but it could be what you're eating is lacking something you need -- sometimes people who lack certain nutrients get weird cravings and odd reactions. Could also just be something completely different, could even be something psychological, as that could also be a factor in why you need to be on a diet in the first place. There's no loss in not eating coconut, by the way -- very high in saturated fat and not all that high in nutritional value, though it does have a few antioxidants in it. It's a fad. I'm guessing in the end we'll find the coconut industry behind the very odd fixation on it all of a sudden.
the keto diet is a great way to lose weight, but it will leave your body lacking in nutrients. I wouldn't try making a "keto cookie" with coconut flour, but just keep to your diet and give yourself a reward on the weekends. I found some great treats at Trader Joes and Sprouts that are within the diets guidelines that are great for everyday (dark chocolates, protein bread that has almost no carbs, keto friendly pizza!).
you probably feel like throwing up because your body is lacking something. I would also suggest taking vitamins