I have had exactly the same kind of existential anxiety from a very young age (I remember discussing this extensively with my parents at ~7 year old). It used to be something that only happened late at night when I was alone - until the first time it hit me in a completely normal situation. I was literally mid conversation and suddenly all I could think about was my inevitable mortality. I can not describe the feeling of shock and helplessness. The floor disappeared beneath me.
I walk out of the house every morning and look at the people in the street, and I just don't understand how they can function normally in the face of certain death. Terminally ill people are often anxious because they're going to die. But everyone is going to die. We are all terminally ill with this fatal disease called "life".
It's nothing to do with wanting to accomplish more before I die. It's the very idea of not existing that I can't comprehend. I'm sure anyone would agree that the world ending would be a fairly grim prospect. When you die, the world ends. Game over, even if everyone else continues.
Alcohol is a wonderful escape from an over-active mind, but guzzling a substance that's likely to screw with your health long term... isn't exactly ideal for an existentialist and hypochondriac. SSRIs seem to help regulate things until - months in - you realise they are actually pretty nasty drugs with too many observable side effects to count on both hands.
Maybe shrooms are the answer, indeed, though having never dared touch them from - strangely enough, fear of their inducing a panic attack - I've yet to be able to comment on that.