Hi... this is a common occurrence and you basically just need to push through it until you start to develop calluses on your fingertips.
This usually involves getting deep ruts in your fingers at first. Then gradually finding yourself peeling damaged skin off. Then as the finger starts to heal, it builds up to almost a harder skin of it's own.
I go through it every time I pick up an acoustic guitar after playing electric for a few months. For the first few days my fingers are killing me.
But you just keep torturing yourself until the fingers start to peel. Within a couple of days it's gotten a little better. By the end of the week, you're wondering why it was hurting so much when you first started.