Sore guitar fingers are a problem when you are just starting out with guitar lessons.
When I first started playing guitar I had a steel-string guitar and I practiced Led Zeppelin’s “Over the Hills and Far Away” for hours at a time and barely stopped even to eat or sleep for a week straight. That was the very first song I learned and I learned it quite quickly, but my fingers have never hurt so much and at one point I basically was making my fingertips bleed. Eventually I had no choice but to take a break until I could binge-practice some more once my poor fingertips healed.
First starting out on guitar—even with nylon strings, which are a bit more forgiving than their steel-string counterparts—your fingers will get sore. It is simply a biological reality! Unless you are regularly using your fingertips for some other activity, like perhaps piano playing, when you come to the guitar your fingertips will be very soft and it will take a bit of time to develop calluses so your fingers won’t be so sore any longer.
Calluses are essentially your fingers’ way of healing and protecting themselves from ongoing damage. But if you play too much, like I did with Led Zeppelin, then your fingers will skip straight past the callus stage and you’ll instead develop blisters, sores, and you can even cause your fingers to bleed—which is not a good thing.
Thus the key within your first two or three weeks of playing is to play enough that your fingers need to recover (which is how calluses begin to develop), but not to play so much that your fingers cannot heal. (After two or three weeks you should start to feel that rough skin on your fingertips: your calluses will finally start coming in.) So practice to your heart’s content, until your fingers are sore, and then, like with so many other activities when our bodies are telling us enough is enough, take a break. This kind of work-rest pattern is one that is good to learn early as it can benefit so many areas in music: practice, learning repertoire, posture, and more.
Play hard, but know when your body is saying it’s time for a rest.