Feary,

What are you doing is wishing the emotions will go away. But they will not. They are shouting in your ears (mind actually) - I think I am going to die (or grow old). And you are just putting fingers in ears, wishing them away. They feel ignored and they shout louder and you then dig your fingers deeper into your ears wondering why this is happening to you.

Remember, they are not your enemies, they are part of you. You are treating them like terrorists bent on destroying you. But they are "you" as much as your "rational part".

The key to lessen the anxiety is not ignoring it (and hoping it will go away), but trying to understand it. Did you ask your feelings why do they fear that you will die? Growing old is normal, but ask them why they fear you growing old. The more you understand, the closer you will get to the solution.

Do this exercise: Sit with a writing pad and write whatever they are telling you. First the language will be abusive because you have been ignoring them for so long (it's equivalent to asking a child to shut up whenever she talks, for years). Try to understand why they are saying what they are saying, ask them why they fear what they fear.
Just this exercise alone will lessen your anxiety, I promise.