Sorry for the morbid subject matter, but I have been thinking a lot more about this since my DB passed away last year from bowel cancer at 34.
I know there is absolutely nothing that can be done about death/dying, but the more I think deeply about the actual reality of oblivion and dying, the more freaked out I feel.
There was a great reply that was posted in response to someone on Reddit's similar fears:
'Non-existence is an unimaginable concept. There are two things the mind can't truly comprehend. The first is the infinite. The second is its inverse, the null. And to try to imagine the null, especially in context to your "self", is fucking daunting. It's like standing at the edge of a fathomless dark pit and looking over it and feeling like you may loose your balance and fall in.
This is the existential dread. It is an empty yawning cave. And there is no examination of it that you will find solace in. There is no empty quip that can fix it, not if you've really hit the deep examined thanatophobia. And the more you think about it the worse it will become. In this sense it is anti-intellectual. I've always felt this was what Nietzche was talking about when he mentioned staring into the abyss and having it stare back.'
I totally get the 'staring into the abyss and having it stare back.' It is unfathomable, and not the best thing to be worrying about on a Tuesday lunchtime... 
I guess there is nothing to comprehend or fear in a way, as death is just that: nothingness. I don't need to worry about something I won't experience, and as the infamous Monty Python song say: 'You know, you come from nothing - you're going back to nothing. What have you lost? Nothing!'
So AIBU in worrying about nothing..?!