I had a lot of problems with cuts on my fingertips when I went busking in winter. The best protection was a good hand cream. You rub it in well and when it's dry, you have protection for four or five hours. When I got those deep cuts, (which can sting like Hell and be a bit messy if they open and start bleeding over the strings), the best cure was to rub a good baby wound protection cream into them at night. It would usually close up the cuts by the morning. That stuff which is used for cracked lips will also do the trick. It is called Lipsil in Britain and Labello here in Germany. It may have another name where you are.
   The other thing I was careful about was to try not to wash my hands too often when I was out. The water tended to dry and harden the skin. That led to cracking. I do not know the source of your problems, so my own experience may or may not be relevant to you.