So you have a problem.
All problems are feelings.
In your case the feeling is one of a discrepancy between the way things are and the way you'd like them to be.
You'd like to be immortal and you realize you're mortal.
You imagine things about what that means.
What does death mean?
It means the absence of life.
Certainly if you're dead you won't be perturbed, as you'll not be.
So it isn't really the business of being dead that you find disturbing, but rather the contemplation of deadness in the here and now.
You can change the way you think about it without denying its eventuality.
Before you were born you were effectively non-existent.
Dead.
After you die it will be the same.
So you certainly don't fear the past, where you didn't exist, so why fear the future where you will not exist either?
Perhaps it's a sense of lost opportunity.
You could think of whether it is true that experiences bring gain.
Suppose they don't.
Suppose it's an illusion, that these various stimulations which existence provides will bring about a sense of "ahhh, that's better than not having these"
Perhaps you could examine the self.
Do you have a continuous self now?
Are you the same you that was the infant?
Are you the young man that you were when you were ten?
Or are both of these individuals dead, and you possess their memories.
Perhaps you are nothing but a series of snapshots and the "self" is just a series of these notes played in a certain sequence.
Visit the cemetary near you. Look at the stones, and the names.
See your own.
What's the difference between you above them and the decayed bodies below the surface.
Go for a walk along a highway.
See a recent carcass of an animal.
Go by and see it again and again until it's gone.
Know that will happen to the body your sensation of self for the moment resides in.
Look at the sky at night when you can see the stars.
Know that some of these have already burned out and what you see are visual echoes of dead stars.
Know that if you were a star and gave off light, perhaps someone far away would see you shine and think...But are they still alive...one day they will die.
Explore the ways others have dealt with death and dying.
Know that feelings are impermanent - both good and bad feelings. The worst of these estimated to pass in at most 3-4 months. The best of these fade too.
You remain you.
And then you die.
All the time.
Sometimes you notice, and sometimes not.
Death comes and flakes you away like a soap bar in the water.
The image fades through the soap.
Ask yourself if others are living.
Ask yourself if you want to know the truth of be content with a lie.
Jesus himself said in John 12:24 - "most truly I say to you, unless a grain of wheat falls into the ground and dies, it remains just one grain; but if it dies, it then bears much fruit. He that is fond of his soul destroys it..." in so saying this, he indicated among other things that the business of true living involves death.
Fighting a natural process is self destructive.
The answer to death is to embrace change and become something new, something more.
If you spend yourself in this way being true to whatever grain of "wheat" you happen to be, then when you die, there will be no loss - not for you or anyone else.
This universe isn't a bag with holes.
What happens in Vegas, stays in Vegas.