It just takes time to build up those calluses on the finger tips. A week or two should help and maybe take a break of two days just to let them heal. I can remember playing until the skin actually came off my fingers many times when I first started. It's normal. One thing that makes it easier though is to lower the action on your strings and even downtune your entire guitar a full step (eg E to D). This will make the strings easier to bend and having lower action will mean you dont have to press so far to get them to the fretboard. Also, make sure you arent squeezing the strings too hard. That was something I used to do, if you look a t most shredders and advanced players you will see that their fingers barely move, they also don't squeeze very hard.
Hope that helps!
Dave