Yes you have to worry about it. As soon as your iPhone gets scratched, It means your iPhones time on this planet is coming to an end, and nothing can stop it from going to the beyond.
of course you don't 🙂 my iPhone doesn't have a scratch yet 😕 after 3 weeks of usage. My iPad now has scratches but I can't see them unless i hold it at an angle but once i get my fingerprints all over it then i forget all about it 🙂 Of course if this happened the week i got my iPad i'd probably have fainted on the spot 😱
It's normal to get scratches, If your worried get some screen protectors. Theres alot of good makes but I found that cheap 10 packs for about £1 on ebay work just as good. The protectors get scratched like mad in your pocket but hey its only a cheap bit of plastic and not your iPhones nice shiny smooth screen 🙂