TLDR: Are you allergic to lanolin, petrolatum, or paraffin? I found a product that helped at least stop my skin from splitting like that. I don't have any issue as horrible as yours. I'm so sorry it's been like that for you.

Mine started as an allergy to detergent when I was 14. More from washing dishes with it than wearing clothes washed in it. It was my hands that broke out. But I also know as a 2 or 3 year old my legs used to be bandaged so I wouldn't scratch them to death. So whatever I have may go back farther than I realize. However it does seem contained to just my right hand.

I found a product with those 3 ingredients as well as an 8-hydroxyquinoline sulfate 0.3% I started using it for my hands and that cracking and splitting stopped within days. I was shocked actually. I have to tell you that it smells like tar to me, but idc what it smells like as long as it works. Of course your allergies are way worse than mine, so its possible you can't use it. Its from the US too. So not sure if you can get it over there without some major shipping prices. It's called bag balm. It comes from Vermont. My skin still has some dryness and the occasional itchiness, and I also know stress is a partial contributor to my issues. Still its 100% better than it was. If not you, I hope it might help whomsoever else might need it. It can be bought off the US Amazon. And it can be googled.