Hi, thought I'd put in my suggestions.
An article in this week's Daily Mail health section gave me food for thought. The writer suffered from this and said it could be an ingredient in liquid soap, namely methylisothlazolinone. EU regulations apparently now permit higher concentrations of this stuff in soaps, foundations, eye shadows, moisturisers, shampoo and conditioner, baby wipes and bubble baths!! Seems there's no escape from it.
Be careful of some emollients, check the labels.
I have now stopped using liquid soap (and I have a carrier bag of the products from M&S, probably now useless!), because I can't stand these painful splits. I also have a red itchy patch in the palm of my left hand, probably where I wash my hair.
So what I do (because I wash my hands so much), is use a latex glove when going to the loo, use up liquid soap to clean it, then use a bar of soap to wash my hands afterwards. TMI probably, but hope the idea helps.
For cleaning, I have gone back to using baby bath (again, check label), and/or Cetraben (get your GP to prescribe if you get free scrips). As a frequent typist, I find it so difficult when many of my fingers are affected. I get through so many plasters and I also use the microporous tape as quite often they bleed. Use rubber gloves wherever and whenever possible if washing up.
Hope this information is of use.