Oy. When I was younger I weighed 198 pounds. I lost 80 of it in my mid twenties and have maintained the same weight over the years. I gained last time I treated but I lost the weight right after.
Anywho, there are lots of foods that meet the fat requirement that don't take up a lot of room and aren't processed or junk food. In fact, off hand I can't really think of anything that wouldn't fit. I am referring to things like a giant tablespoon of walnut butter, or almond butter, avocado, a handful of nuts, a couple of chunks of cheese and so on. Either way the fat requirement is gross but there is still lots of foods you can tolerate.
I reduced my carb intake considerably & increased the veggies since I was not sure how my body would respond to a drastic change in intake. It turns out I lost 13 pounds that I couldn't really afford to lose - and gained a little acid reflux in the process. I discovered I could not eat that kind of food past 10:00 at night.
You may have to do similar juggling. I know the last thing you probably feel like doing right now is experimenting but you may have to since you are likely eating the kind of food you have not had in a long time. It takes a while to get into a groove that works for you. By week 7 or so I adopted most of the ideas and suggestions I discarded in the beginning.
I am not sure why you are sick as a dog. Do you mean you cannot tolerate any kind of fat? Remember there are good fats and the lesser healthy fats. There are lots of posts related to this topic however.
One other thing is to try to remain active. By that I mean not sedentary. I had lots of blow off days when I was on the Incivek but I always felt better after I walked my dogs or did the stairmaster or even worked in the yard.