Sounds like you are going through the difficult adjustment period when we think in terms of what we can't eat, rather than what we can.
I suggest you have a look at the low carb food lists listed in the low carb section of the forum. The list is impressively long, and the portions of those foods can be huge, satisfying and stay low carb.
And as for fat intake, have a look at the recipes on the
www.dietdoctor.com website. When you do, make a note of the fat content, and the carb proportions. You will find meals often involve olive oil, mayo and butter in the same meal. For cooking and serving. Seems a horrendous amount to start with. It isn't. Just a matter of swapping carbs for fats so we dont go hungry. Plus it shows that good quality fat is acceptable and guiltfree.
From the sound of things you are getting hungry and craving carbs because you aren't eating low enough carbs and high enough fat.
Don't worry. You will get there. It is just a huge adjustment, to start with.