Just meeting a Shoggoth is not in itself horrific. Rather, it is a question of placement. The key to good mythos horror is to take the familiar and and introduce the terrifying into the familiar in a shocking way: things not working as they should, places being where they aren't supposed to be, and things challenging your assumptions about how the world/your body/science/religion etc. should work. 

Items of electronics that turn on by themselves. Books that follow you. Things seen out of the corner of the eye. All of these and more create a slow deterioration of one's nerves.

Then you build up that sense of wrongness into some kind of shattering revelation that what you believed about life and existence is pure fantasy (i.e. that you're not real, or that you're real but not human, or that you're human but no one else around you is, or that your life is an illusion, or history, or that you've been manipulated your whole life for some sinister purpose, things that seemed normal and good are in fact terribly wrong, and you have no one to turn to).

One possibility for "alternate mythii" is that the mythos wasn't real, until Lovecraft wrote it and people started to read it. Now it becomes more real every day as more and more people read the books and play the rpgs.. and only you know the destruction that people are leading themselves to.

Worse, you can't just tell everyone, because it is that very belief that will strengthen the mythos. If everyone on earth knew the truth, the Great Old Ones would immediately manifest.

Right now there still may be a chance, but what to do? what do you do?

Oh, and the Great Old Ones.. they know you know.