Welcome!
I'd try persisting with the book. It's a way of eating really, not a diet as such.
Low fat foods are to be avoided as they often contain added sugar or other nasties. I don't think that there is anything wrong with low fat milk in itself, although not sure why the full fat version makes you feel ill. Full fat options will make you feel fuller quicker, so you'll be less tempted to snack.
If you're cooking everything from scratch, reducing sugar and wheat and avoiding veg oils you are on the right track.
Try introducing yourself to the foods you're not keen on gradually perhaps? Experiment with different ways of cooking?
I bought some cavolo Nero which I don't cook with often - it's currently in my slow cooker with some stock, cream, Parmesan rind, leeksand onions. Might not be great, o t oh might be a new addition to the repertoire ! Time will tell...