When you first start playing a guitar one of the things you will notice is that the skin on your finger tips will harden and to start with might release some skin and feel worn, after a few months of playing (if it hurts stop playing and wait a few days) When your fingers harden you will notice that they still hurt after a few hours but that’s normal and it’s just a sign to take a break, playing for many hours is ok if you alternate between finger frets and chords which can lighten the feel on your fingertips.
If you cut your fingers you will be surprised how quickly they heal. Rest your fingers and try again when the cut has healed.