I don't have any suggestions of products that would help.
I had an absolutely TERRIBLE time with the insanely dry air in southwestern states where I lived. Not only did my skin split like that, but I always had blood all over my face from the dry air. Such a lovely look, right?
I spent a small fortune on various products, and generally used huge amounts of Chapstick but it hardly helped at all.
Louisiana, on the other hand, has some of the most humid air in the country! My skin absolutely loves the climate here. I use no lotions or other products and don't even own a Chapstick. My skin looks and feels great!!!. For me, our humidity is one of the big "plusses" of living here and retirement in Louisiana solved the problem.
I try to keep my mouth shut when people online badmouth the high humidity in my state.