Welcome abourd dude. Your fingers will stop hurting once you build up some calluses, which can take anywhere from 2 days to a week depending on how much you practice, and how harsh you are with fretting (like doing bends, vibrato, slides, which you probably haven't learnt about just yet.) As far as gritting through the pain, the last thing you want to do is play with pain, it will make a problem worse. Though, since your just building calluses, this is probably one of the only times you can play through the pain. I did when I first started and my calluses came in no time.