You are likely in deep ketosis, which will suppress your appetite utterly. When I first went very low-carb and was in deep ketosis, I was accidentally only eating 900 calories because I was not at all hungry (or so I thought). Eventually I passed out on the sidewalk. Not good.

You MUST eat more...800 calories will NOT sustain you! And with only 800 calories, you're almost certainly not eating enough carbs to stay out of ketosis and thus avoid such intense appetite suppression. Your brain isn't getting the signal that you need to eat.

Checking with a doctor is not a bad idea, but in the meantime add some calories to your day even if you're not hungry. You need food but can't feel it. You're hungrier than you realize. Trust me!! And let us know how you do!

I'm not a trained professional, but clearly something's not right.

It might help if you share your age, activity level and any general health history that's relevant? What foods comprise your 800 calories, which is of course extremely low?

Being light-headed can be benign, as in postural hypotension when you stand up (I had this when young and it's nothing to worry about.) Or, it could signal that you are malnourished or deficient in important nutrients.

Lack of appetite is worrisome only because you are eating so little and light-headed. Have you seen a doctor lately?

Are you the only Paleo in your house? I am that way and it can make it hard to find the proper food when everything around the house is not Paleo. You need more variety in your diet. I have a similar issue. However I also eat eggs. Meat alone will not be enough. It takes awhile to find your sweet spot for eating. I also eat veggies and fruit and vanilla ice cream. I would also eat chocolate ice cream but I can't because of allergies. Potatoes would be a very helpful food. Every meal have at least two macros. Fat, protein and carbs. So if you are eating meat you have a veggie or butter or bacon. If you have eggs also have butter, veggies, bacon (even better have all three.)

Eat when you are not hungry. Your body can handle the extra food. The addage eat when you are hungry does not apply in this case. Do plan on eating at regular meals with larger portions due to more varied food.

It sounds like you're getting a serious dose of satiety hormones (leptin and/or PYY) from the protein (and fat?). Maybe try starting your meals with carbs, like fruit or root vegetables, before eating the meat, which causes the PYY & leptin release that kills your appetite.

That much athletic activity on so few calories is worrisome from numerous angles. You're young and you may be wild, but your practices are not healthy, or more aptly, not healthful. Google Karen Carpenter, for the fun of it. If what you read isn't fun, take that as a good sign.

You run everyday so you need more carbs. You don't need to be in ketosis. Eat up all the whole foods you want whilst keeping those processed carbs out.

If you continue running and eating only 800 calories daily you'll be stripping your muscle mass which you don't want.

Try eating more fat and less protein. The meats you eat all are high in protein and low in fat. You can overdo it with protein depending on your metabolism, and meats take longer than carbs to leave the stomach, thus leaving you fuller longer. Since you're very physically active and not eating nearly enough calories, my guess is the light-headedness is from hypoglycemia. If you eat enough protein and fat without any carbs most people can avoid this because the body starts gluconeogenesis to stabilize your blood sugar level. But you seem to have cut out both fat and most carbs, which will lower both your blood sugar levels and your metabolism. Do you eat fat with your meals? I'd recommend eating more fat and carbs in the form of starches like sweet potatoes or yams. Everyone is different in terms of macronutrient needs, what's important is that you cut out high sugar foods and drinks and other harmful substances like artificial sweeteners and caffeine. The way you can find out what works for you is to try different ratios of carbs and protein and observe if you have more energy or not. If you felt the need to binge eat that could indicate a nutrient deficiency, some degree of metabolic problems, bacterial dysbiosis, or too much stress in your life. But your goal should be to increase your calories and go from there.

Take a potassium supplement with each meal and chelated magnesium twice a day. I had the same problem, my Dr tried to put me on blood pressure medication but the warnings and side effects scared me so I started taking potassium and magnesium and the issues went away. I also stopped counting calories. I just make sure I get protein (2-3 oz), fat (a few nuts or tablespoon fat) and a huge serving of low carb veggies at each meal (and a cup of berries with breakfast). I eat about 4-5 times a day. Read The Protein Power Lifeplan by the Eades. Good luck!