I have always believed that many people think that they have a smaller range than they actually (or potentially) have. It's a matter of exploring your range (preferably in private!) and practicing.

Try learning a song which you believe to be 'outside' of your range and work at ways of hitting the high notes without strain. Simple things like lowering your chin before the high note can make a big difference - counter-intuitive, I know, but it works!
More importantly, make sure that you have enough breath before the high note, and that it's coming from your diaphragm, NOT your head. This involves working out a breathing 'strategy' for each song that you sing. None of this is particularly difficult - it just requires thought and practice, practice, practice ...