I don't know how drastically P90X restricts carbs and fats, but combining extremely low-carb, with extremely low-fat, can be uncomfortable, unhealthy, and even dangerous (google "rabbit starvation" or "protein poisoning"). It's been reported that people sicken and die quicker on such a diet than they would on no food at all.
(In theory, at least), if you're going to cut carbs to an extremely low level, you have to add at least moderate levels of fat. To some degree, the lower carb/fat you go, the more water you should drink (but that too can be overdone).
Moderately low-carb and moderately low-fat may be healthiest (South Beach and many ancestor/paleo diets are examples of this).
I think really experimentation is all most of us are left with. Write down everything you eat and experience. If you experience negative effects like severe headaches or dizziness, listen to your body and adjust your diet until you find what helps.