I have severe insulin resistance as a result of PCOS. I was on medication for it when I was first diagnosed because it was so bad. I was told my by doctor that I needed to opt for a diet high in animal protein to control it, but that DID NOT sit well with me as a way of eating that would be good for me in the long run.
After doing a lot of research, I decided to adopt a vegetarian diet. My doctor was upset by this; however, when I went back in for blood work after two months on my new diet, my insulin levels were completely normal and I was taken off all medication. My doctor was completely shocked.
That was 16 years ago, and I have since made the transition to vegan, eating no meat, dairy or eggs; only fruits, veggies, legumes and whole grains. I even grind my own flour and make all our bread. I have controlled my insulin resistance entirely with my diet and exercise. You don't have to give up carbs, you just have to be smart about them. I know that if I eat anything white (sugar, flour, rice, potatoes), I will be sick almost immediately with horrible headaches, nausea, dizziness and tired-feeling.
Several of my insulin resistance/PCOS symptoms - brown patches, skin tags, irregular periods, acne - didn't improve at all until I became vegan, at which time they all disappeared entirely. However, I know that not many are keen to make that kind of lifestyle change!
From my experience, I don't find that you have to 100% eliminate something, but definitely restrict anything processed, refined sugars, white flour, white rice and starchy potatoes, like Russets. I still have birthday cake and a cookie now and then, but only a few times a year. I know how gross I feel after I eat that kind of thing, so it's pretty easy to stay away! I don't have a reaction to any type of whole food at all, even the whole wheat bread I make. I can have a piece of that, and it doesn't affect me at all.
I suggest playing around with your diet a little and see what works for you. That's what I did after doing some research. Insulin resistance is really the pits!