I’m wondering if it is truly even possible to eat just healthy food in general, forget about keto and carnivore, for $12.50/week?
Costs as a carnivore: Where I live, cheap ground beef is $2.99/pound on sale. With a pound of ground beef a day plus some eggs to fill in extra, let’s say 1/2 dozen, that could already be costing about $4-5.00/day. We are talking $28-35/week. I can get chicken leg quarters pretty cheap, about $0.80/pound for a 10/lb bag. Let’s say 1.5 pounds of chicken a day and still the 1/2 dozen eggs. Now we’re talking about $3.20/day or $22.40 a week. Eating carnivore for $12.50/week is just not possible.
Canned meat and fish are not cheap. I live in Northern Virginia, a tin of sardines is pushing $3, I think. New York City is going to cost more than Northern VA. If you worked out the price per pound, I can’t imagine they would really be any cheaper than buying cheap ground beef and cheap chicken.
Keto would not be much better. The OP could possibly get away with lower protein, but for a normal person, who does not need therapeutic keto for medical issues, I think eating a tiny amount of protein and tiny amounts of vegetables a day plus tons of cheap fat would cause vitamin and mineral deficiencies over time. Plus, she is working full-time, would she really have time to go all over the place trying to find cheap sources of meat or fat?
So after all these ponderings, it brings me to the original question:
I would try eliminating the things that are known to be the most common allergenic foods: wheat and dairy. That could still leave plenty of foods, some protein, some cheaper food sources like rice and beans, less expensive fruits and veggies, and see if you notice any health benefits just from removing those foods. And then take it from there. If it makes difference, leave it out, if not, put it back in and try removing something else like eggs, nuts, soy…
Just removing gluten containing foods which are the foods that mostly tend to be junk and/or sugar filled would certainly put you in the right direction. Maybe you don’t need to go all the way to carnivore.