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My son is sensitive to wheat/gluten and showed similar behavior to your son's. He also does this when he has a low blood sugar level ( he has diabetes too). I wonder if your son is experiencing episodes of low blood sugar from poor absorption due to celiac, and hence the "munchies" type behavior?
After going gluten free, my son's aggressive eating attitude, and constant hunger abated, and is rarely a problem now. His blood sugar profile has greatly improved too.
I have read in various places, that some celiacs cannot tolerate any starchy type foods and grains for quite a while, until their gut is totally healed. It can appear that they are intolerant of many foods, but this is because the gut needs time to heal, and most starches may need to be avoided in the early stages. See the Specific Carbohydrate Diet books, by Elaine Gottschall (and there's another author) which, I believe, are also gluten free. They may contain helpful info for you in the early days with your daughter, and possibly in the longterm.
Also, have you had her checked for T1 diabetes? Sometimes the conditions co-exist.
I feel for you, and hope things improve soon for you and your baby girl. Don't be afraid of taking her back to the doctor, even if it's just for peace of mind.