You could try paleo or other low carbohydrate options. I'm very picky as well and have issues with some food textures (mushrooms for example...). You could keep eating all the protein that you like (chicken, steak etc.), apples and other fruit as well as sweet potatoes if you choose to go more primal than paleo. I'm not allowed to link but if you google "Mark's Daily Apple" you'll find a lot of info about primal diet on his site. It will help you lose weight and it's very healthy too.
Good luck with your weight loss whichever diet you choose!