!!! I'm celiac too! (along with fun crap like ulcerative colitis + lactose intolerance) if you have any secrets to baking i would love to know!
generally I make gentle curries/soup non-stop, that's my way out of the restrictions hahaa
Oof, yeah, that doesn't sound like a fun combination! I'm lucky that my other autoimmune stuff doesn't come with any additional dietary restrictions (type 1 diabetes and a hypothyroid thing) so I only have gluten to worry about. But I know delicious gluten-free, dairy-free stuff is possible because there's a bakery here that is both - and for the first year that I was eating their stuff I had NO idea it was also dairy-free.
My main baking advice is basically: find a decent gluten-free replacement flour if you can (I don't know if the ulcerative colitis prevents certain foods) because it's SO much easier than buying like four kinds of flour and combining them. I don't bake a ton of really complicated things like cakes though (mostly cookies) so I don't know if it will work for everything. A lot of flour mixes will have advice on the package.
I also find that gluten-free oats (if you can tolerate them - I know not everyone can) can help with the texture of cookies. My favorite recipe is for gluten-free oatmeal white chocolate cranberry cookies, and I think the oats keep them from having the grainy texture you sometimes get with gluten-free baking. They'd probably be pretty easy to make dairy-free too, if you used shortening or lard instead of butter and found dairy-free chocolate chips (which I know exist.)
Also, in poking around for butter substitutes just now, I found
this article on the subject which might be helpful. (I bookmarked it for my own use, because who knows, maybe I'll need to bake for a dairy-free person at some point!)