I have Hashimoto's and really dry skin (my scalp is horrible, too). The digestive issues could be a factor, if you're not really absorbing nutrients properly. Paleo is good for you, in-general, but I think it moreso works with "clearing up" skin, like with acne, rosacea, and so-on. I recently started getting into Asian skincare, as they focus on lots of light layers of hydration. My skin used to scale and flake, but now it's nice and soft!

I use a low PH face wash only once a day. Too much cleansing can rid your skin of it's natural oils. I swap between this Cerave cleanser and this Hada Labo one. Then I use this lotion (which is more of like a serum) and this gel moisturizer.

I'd suggest reading into the science behind humectants, occlusives, and emollients. Example, you can use a lotion, but if it doesn't have any type of occlusive ingredients, the product and all the moisture will just evaporate/dissipate; it needs something to seal it in. And as much as Asian skincare seems like a million steps, you can really work with just 3 or so products.