Good for you! We went cold turkey off of 21 foods for our daughter five years ago. You have SO many more choices and options now. Taking her off both is important when dealing with this kind of thing because it is not a matter of it been an allergy but an inflammatory to the brain in this case. You can do it and there are lots of things to help you.
My daughter is extremely picky. What you can tell you daughter is that over time her skin will look better, she will feel better and not be so moody. You'll learn to point out the differences and hopefully she will start to notice them. With mine, she was like Dr. Jeckell and Mr. Hyde when she ate gluten. Her grades were in the low 'C's - now she is a typical teenager and she got off all of her asthma medication. Be aware that vaccines have these ingredients in them so do your research and read the package inserts.
Now, what to do and how to do it. As I said, I went cold turkey and remove everything from the house. Please go to www.tacanow.org to the GF-CF Diet section. You will find EVERYTHING you need to know there, hidden sources, alternatives, recipes, and the all important - where can you eat out.
We have no egg and no soy (these two are the worse for my daughter) along with no yeast now. She eats at Rubios (corn torillas, no cheese on anything, lots of guacamole), Red Robin and Islands /hamburger patty and fries, In N Out is the best for these - just think protein style. PF Changs has a gluten free menu as well as many other places. You'll find more at the TACA site.
Contact me anytime if you want to talk about this. You are doing the right thing for her, especially over the long run. It is going to be hard because she is use to things but especially because she is a teenager. Mine is almost 15 too. Mom, it will be extremely beneficial for you to do this as well. You will not feel bloaty, moody, aches will go away, sleep better....