Sounds like a bit of an existentialist crisis. I believe its may actually be called existential death anxiety. On one hand, yes its disturbing, on the other, its a testament to how far we have come as a species in that we are extremely self aware.
But that's not comforting in the slightest.
The problem is there is not a great deal that can be done about it. Therefore emphasis must be placed upon making the most of it no?
Good news is that death anxiety declines massively as we live beyond 65, so it should get better.
There probably people who you can speak to, if its a big problem. Freud would argue that its a mask for another issue in your life that you aren't ready to confront. But there are support groups for all sorts of things, one would imagine this is no exception!