You're getting good information here, and I endorse everything above. Since this is so new and bewildering (and it always is, we all began there), let me add a note or two of historical perspective to help put it in a little better focus.
The low-fat high-carb mantra is yesterday's traditional wisdom. A lot of it comes from the fat-is-bad-for-you rule that we've been indoctrinated with for the past half century or so. Trouble is, that formula is more politics than science, and in fact the science is calling it further and further into question these days. Which is a long winded way of saying that your CDE is preaching the old gospel and your doctor sounds much more up to date.
As Terry says, diabetes, in whatever form and at whatever level, is a disease of carbohydrate intolerance. If carbs are the problem, then the fewer of them you have to process, the better control you'll have. This reasoning seems so obvious that it's at the level of two plus two equals four.
That being said, each physiology is distinct and individual and the amount of dietary carbohydrate that produces the best result is likely to be different for each of us. But the general rule is, less is better.