Re: Some help please for my dear mum:)
^ cracks on fingertips not corners of the mouth is being asked I think. Two different conditions.
Gloves and any oil or moisturizer on regular basis is fine for hands. Just keeping hands warm helps too. Wudu with good warm water and cover hands quickly.
Washing hands too many times should also be avoided. Soap may need to be changed as well.
I don't think a doctor is needed based on the question.