Is it possible you have eczema/dyshidrosis? If it's an autoimmune issue, then reducing your overall allergic load should help, as will sparing use of steroid creams. Sun exposure usually helps too, if it's not too cold where you are.

Also make sure you're hydrating enough from the inside. It's always hard for me to drink enough water when I'm cold.

And +1 on checking the ingredients of your hand cream. If you're sensitive to an ingredient it will only make things worse; IME petroleum based creams damage the skin and get me "addicted" to them. Pure shea butter before bed works well for me, too - it's too heavy to use throughout the day if you need to be touching phone screens and/or computer keyboards, but if there are days when you're onsite using fiber-based information storage systems you could use shea butter any time.