Don't get the fat-free. You will probably notice, if you look at the ingredients, that it has a little list of starches added to it (stabilizers). The 1%, at least the brand that I buy, has in fact slightly fewer calories than the fat-free, a touch more fat, yes, but fewer carbs.
Cottage cheese (and most other dairy) does naturally have some sugars in it, lactose ones. However, bodybuilders and other athletes have been eating cottage cheese as a pre-bed meal for years. If your diet is otherwise clean, I wouldn't worry about it; likewise natural fruit sugars. Unless you are doing something drastic, like a competition diet, there is no reason to get crazy and eliminate every source of "sugar"; just get rid of added sugars where you can (and don't eat those before bed).
