First: What have your macronutrient ratios been like? How low carb have you been eating?
When you say you've been eating "at least" a half-pound of meat every day, that suggests to me you often eat significantly more. I'm a pretty happy carnivore, but most days I don't eat near that much meat, and there are a lot of days when I eat eggs, but no meat at all. So maybe it's just time for a break from so much meat?
Second: It might not be diet that's triggering your headaches and sleeplessness, and your sudden aversion to meat may be in response to feeling unwell, rather than strictly a diet problem.
Is there anything else going on in your home or work environment? Any possible stressors that weren't present before? Anything that's changed that doesn't seem like a stressor--but could be? Stuff I'm thinking of includes different/harsher lighting, a paint job or new carpet, etc.
[ETA: Also consider anything that might be a new source of muscle tension in the neck and shoulders (leading to headaches and difficulty getting to sleep). A new chair at work? Sitting in a different position? Driving a different car, where the seat isn't quite adjusted right for you? That sort of thing.
And last, but not least--reaction to a previously-unknown allergen. My eyes have felt like someone poured sand in them for the last three weeks, and it took me almost that long to realize it's the cottonwoods at my volunteer gig that are doing it. I haven't had any sinus/respiratory trouble, so at first I thought I might have some kind of infection in my eyes, but no--it's the cottonwoods. And they've made me feel a little headache-y, too. So there's another one to consider, especially since it's springtime and your headaches are sudden-onset.]
Sorry I can't be more help, but these are the first things that come to my mind.