Cat feces everywhere

I don't know what is wrong with my cat. She simply refuses to poop in her box, and it is making me physically ill. This has been going on for a couple months now. We have taken her to the vet, twice. The only thing he found wrong with her is a high level of bacteria in her feces. He said that this might be giving her an upset stomach and causing her to have painful bowel movements. He gave us amoxicillin both times which we gave her. The first time it seemed to clear up the problem. The second time he also suggested that we put her on a high fiber diet, since she was having some diarrhea as well. We took the vet's suggestions but it is not working. We have also tried cleaning out the litter box every day but it does no good because she hardly ever uses it. I live in a very small one bedroom apartment. Her litter box is in the kitchen. I really don't have any space for another. Lately she does her business on the carpet in the dining area next to the box. I used to eat in there but I cannot anymore. I feel trapped and constantly nauseous because of the horrific smell and the smell of the chemicals I use to try and get rid of it. I just don't know how much more of this I can take and I don't know what else to do. What could possibly be wrong? The vet does not seem to know. I don't know what to do.

Is her food bowl next to her litter box? Many cats will not go in their litter box if their food is close to it.

nope, the places where she actually goes are closer to the food bowl than the litter box

I would throw out her old box and get her a new one. Sometimes they associate objects with pain, and while she was using the old box she was in pain, so now she just avoids the site that caused her pain.

There is bacteria in her feces and the vet doesn't know how to rid her of it? Here I go back on my GSE soapbox, but if I were you, I would buy a small bottle of Grapefruit Seed Extract and put 3 drops a day in her food. The stuff is liquid, it is very thick and bitter and you can buy it at any good health food store. It will kill any bad bacterial or fungal infection inside the body.

But I would definitely toss out the old litter box and also pick up some Nature's Remedy a good enzyme cleaner, and clean the areas. Hydrogen Peroxide will work too to break down the smell.