Hello Hans Olo
I guess feeling afraid of death is normal and everybody feels like that from time to time- but it sounds like you are very occupied with this topic at the moment. I wonder what the reason might be. Are you or someone you know suffering from a lethal illness? Or have you lost someone? Another reason I could make out for you thinking about death is that your worldview/spiritual believes etc have changed or that you are doubting them?
For me in personal, I remember when I was about twelve and realised for the first time in my life on an emotional level that I am definitely going to die some day. And everytime my mind remembered me of this fact, I got really afraid and couldn't comfort myself (this was after I had decided that I was an atheist, I was brought up Christian).
At the end, I accepted for myself that death is a frightening thing and that I have to accept this fear. But also, from today's view, I'd say: Even though I can't change the fact that I'm afraid, I realise to a certain extent that my fear is irrational: Death means "nothing", you don't feel pain or sth, you just stop to exist. We should be rather afraid about feeling (emotional) pain in our lives, or about getting old and regretting things we missed to do than being afraid of death.
With other words, there is a time to be afraid of death, and it's normal and unevitable that you think about it sometimes, but one should also learn to let loose of this feeling and shift one's attention focus to the things that really matter in life: The pleasures and problems you are having right now.
At least that's what I think. Maybe it sounds kind of pathetic.
Anyway, I hope I could help in that you don't feel so alone with this topic anymore.