It's pretty normal for your fingers to hurt. You will eventually build up some tougher skin on your fingers, but in the meantime you could get some lighter gauge strings. These are generally more flimsy and easier to press down.
If you're guitar hasn't been set up, that could be the perfect thing for you because they will not only replace the strings for you, they might actually be able to lower the action on your guitar (making the strings closer to the fretboard). A set up is usually ~$35 + the cost of strings.
Hope that helps