While I haven't tried the Atkins (and do not promote any special "diets" other than sensible nutrition..as in an actual nutrition course) I would encourage trying to go gluten free for a while...not carb free. Eliminating a possible allergen is different than a fad diet. You need to figure out how YOUR body responds to different types of food. It sounds like you are an intelligent person, with doctors who are less so, or at the very least they are impatient.
I am finishing my 1st week of gluten free, and already feel much better. I didn't have skin issues to begin with really, or so I thought, but have discovered that my skin looks so much better. I didn't realize the dinginess I had, till now.
I know a number of people who can't eat gluten. And I can say that there are a lot of health issues that can be traced back to it, so skin problems aren't out of the question. I have some other issues, that the gluten free seems to be helping (have not been tested for celiac either, I am just taking matters into my own hands and tummy
I just found this blog, she does a better job explaining stuff then a reply would allow. Are you new to gluten-free?
But I would say, if you go gluten free, don't get the prepackaged foods to substitute. At least not at first. They can cause their own set of problems, to put it delicately. There are whole grains that don't have gluten in them. This way you can have bread, minus the icky processed stuff, plus the nutrients and fiber we should all be getting.
I know this wasn't very informative, but I hope it helps in a pep talk kinda way. =0)