The best advice here is to read some comments of NASA scientists who provide solid facts which prove perfectly well that in the near future, there will not be any Doomsday. If it does not help, there are some tips how to handle everything.
First of all, there is a way of calming oneself down by creating perfect surroundings in preparation for This Day. You can buy food supplies enough for a week or two. In this way you’ll have a quite reliable background for surviving. (I mean if you're still obsessed with this idea).
Secondly, you can arrange with your family or friends to be together on this day. So, you’ll have a support. And finally, to have a hope and a strong belief that everything will be OK.
For religious people, the best refutation of Doomsday is that in Bible it is stated that the mankind won’t know an exact date of the day of doom.
Moreover, it is a good advice to watch some movies about world-wide disasters, which, in most cases, have happy-ends.
But still, be sure that everything is going to be all right! As they say, stay calm and keep enjoying to live on such a beautiful Earth!=)