which sentence is right?

Off the top of my head, I might use an alternate version.

and who quickly progresses from stranger to friend to becoming her boyfriend.

But then it's early in the morning where I am.

I would prefer to have the whole sentence presented to me, rather than just the tail end of it. It is hard to access what you have without that, in all honesty. (You don't have to quote yours exactly. Substitute some words, etc.)

Quilliam said:

Overdosed, she ends up in a hospital bed across from Richard, a man who's oblivious to her status and who quickly progresses from stranger to friend to boyfriend.

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For starts, I'd turn it into two sentences.

Overdosed, she ends up in a hospital bed across from Richard. Oblivious to her status he quickly progresses from stranger to friend to boyfriend.

As far as versions, this would be my choice as opposed to using the article "a" and "her." That's just me though. Everyone writes different.

Quilliam said:

Overdosed, she ends up in a hospital bed across from Richard, a man who's oblivious to her status, and who quickly progresses from stranger, to friend, to boyfriend.

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Other than the need for commas, there's nothing at all wrong with this sentence. It reads very well.

Jamesaritchie said:

Overdosed, she ends up in a hospital bed across from Richard, a man who's oblivious to her status, and who quickly progresses from stranger, to friend, to boyfriend.

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Quilliam, your first two commas are spot on. Definitely continue avoiding the automatic comma before "and" unless an independent clause follows, and good writers don't fall into the trap of inserting unnecessary commas to set off prepositional phrases.

I'd vote for the two sentences. The one thing that niggles me a little is the idea of quickly progressing from stranger to friend to boyfriend. Everything is relative, but presumably we are talking a matter of days and not minutes?

It's hard to tell from a single sentence without seeing the rest of the piece, but I had a little trouble reconciling the word "quickly" to that progression.