Carrots are great for you, you could eat pounds of them and not have an excessive amount of calories in your diet. A cup of sliced carrots only has about 50 calories, and a large (2.5 oz) carrot only has about 16 calories.
As for their sugar content, it IS high when you compare it to other veggies, but it is lower than most fruits and lower than most grains (Carb count) plus they are high in fiber.
Eat carrots all day long, and the only problem you'll have is "too much fiber" and probably some bloaty feeling, but you won't mess up your calories for the day with carrots
Anyone who says such a thing is just looking for reasons to avoid them
One thing to remember about eating healthier is this: You're not planning to stop, right? So if you get onto 2000 calories a day (like I try to maintain), then you will be eating a diet which is pretty normal and you would be hard-pressed to gain weight from all that food. Exercise would be likely to help you increase your lean body mass, even if it doesn't show as a dramatic, instantly visible change on your scale.
I come here for help and support with my regular diet; my food plan is not going to be able to change... I just need help staying on it and staying motivated with eating normal foods. I don't diet, and I don't plan to change how I eat after I reach my "goal weight" because that is just as likely to cause me to gain the weight back as it is to turn my views of "food as a reward" back to how they were.
Okay, enough rambling, just know that you can eat all of the carrots you want, even as a binge, if it's just the carrots. If you want them cooked, I highly recommend picking up some butter spray or some of those salad spritzers, they add flavor while keeping the calories reasonable.