so confused about eggs and yogart

I am on my 2 week pre op diet. I have heard ppl say they lived on omelets during this time but there is alot of fat in just a few eggs, and what about greek yogart it has 14g of carb but everyone says that is what they ate. my diet is low carb high protein to make my liver smaller

 You can use egg whites if you're concerned about fat. I go between both. Yogurt has lactose in it, which is a natural sugar. You're better off using plain yogurt, and flavoring to taste, instead of buying pre-fab fruit yogurt flavors. They usually have lots of additional sugar added for sweetness. 

Omelets can be made with Egg Beaters, which is lower in fat.

The carbs from Greek yogurt come from lactose, milk sugar. That is, if you are getting plain, which is what that number sounds like. A glass of milk has 12g of carbs so yogurt isn't much carbier.

Lactose doesn't work the same in your body as sucrose (table sugar). It's a natural form of sugar that your body can metabolize well. Also Greek yogurt has a lot of protein as well so those two nutrients work together to nourish you.

The body needs some carbs. You can't avoid them. For your post-op lifestyle you'll have to learn to eat smarter carbs to fuel you. But if you're worried about yogurt hampering your liver shrinking efforts, talk to your nutritionist about it.

I ate lots of lean meat and fish, such as tuna. Also beans.  How about some non starchy veggies for variety?

One thing that needs to be remembered about the fat in eggs is that the majority of the fats are monounsaturated and polyunsaturated. These are the good fats that your body needs and they help to reduce the total cholesterol and LDL (bad) cholesterols. I have eaten a minimum of 2 eggs a day for years and my cholesterol levels have always been "excellent" (my doctor's phrase). I also eat a fair amount of nuts (cashews, pecans, pistachios) these are also "high" in fat. However, again, they are low in saturated fat and high in unsaturated fats. FYI - saturated fats are solid while unsaturated fats are more liquid in nature. Hope that helps!