For a long time I've been pretty worried about my mortality. But ever since I became a Christian a couple years ago, I've been much more at peace about it. Not all the way (yet?), but much more than before. I highly recommend looking into Christianity to anyone else feeling that same fear.
I've been a Christian for 25 years. I don't think you'll ever be completely at peace with your mortality--in the same way that riding a roller coaster is still scary even though you know it's safe.
But I've seen the difference in the way my Christian and non-Christian friends handle death, and the difference is striking.