You are not eating properly, in my opinion. There is no reason why you should not be eating more kinds of vegetables. Eating only carrots won't give you all the nutrients you need from plants. Also, eating some fruit is good too. If you are not allergic to nuts, also try some coconut oil to cook, in addition to olive oil, and a few almonds/walnuts in the week. And if you can tolerate dairy, go for some home-made goat kefir (it has helped me a lot with IBS).
Have you experimented yet with this way of eating? Or are you just asking if eating this way will help?
My husband started eating the Paleo/Primal way after he saw it working for me. He was "diagnosed" with IBS and had it for nearly two years prior to changing his diet. He had diarrhea on a mostly daily basis; it was terrible. Nothing the doctors did for him worked (his one doctor even told him to avoid broccoli & fiber...what??).
When he started eating Paleo/Primal, his problems started going away! No more constipation or diarrhea! Take that how you will.