I wouldn't know much about it, but is it because you're taking hot showers? That's usually the reason my skin gets dry in the winter.

E45 cream works wonders on dry skin, also anything that can be used on a babies skin, might be an idea to go see a doctor, they might be able to help.

I've heard great things about coconut oil. The only concern I'd have is smelling like coconut, which is not really an issue compared to having dry as hell skin.

I frequent both of these reddits for advice, you might find something useful there, too:
https://www.reddit.com/r/SkincareAddiction/
https://www.reddit.com/r/AsianBeauty/

I usually just use some key words in the search bar, or I check the wiki/guides they have linked. However, your case may require more help than amateurs on a forum. Hopefully there's something useful there for you, though. They have lots of advice regarding different skin types and issues. I don't know if you'll find your answer but you might find a few useful pointers. They're also great about directing you to budget friendly products. If you wanted to, you could try making your own post. They're really helpful, especially on SkincareAddiction. They live for it, haha.

I don't mean to come off as a patronizing, but do you drink a lot of water? Again I think your issues are deeper than just drinking water/using fancy creams but it doesn't hurt to stay heckin' hydrated.

Your best bet is probably the dermatologist but I thought I'd throw in those reddits, just in case you find something.

Yeah, I feel that. I had a really hard time training myself to drink more water. I kept forcing it, and eventually I began to crave it. Now I need many, many cups per day to be comfortable.

I use coconut oil for my hair. I think using it on your skin would be a bad idea. It would just clog your pores

I used to have a huge problem with dry scaly skin on my hands and arms. It turned out to be not only the chemicals I worked with, despite gloves, but also I had an allergy to the dish soap I was using. I stopped using that soap and the problem cleared up really well. You might look at the kinds of detergents you are using on your dishes and clothing as well.