The word you're looking for is novelisation.
I had the dream again, the "Wonderland" dream, as I call it
My steamy tears fogged up my vision and froze to my fur as they slid down my cheeks. The only thing I could do was walk faster in the cold December twilight.
pretentious and masturbatory, there is no reason for our narrator to be poetic about this
I woke up in a cold sweat. Then I remembered what had happened, and I started to weep. Warm tears flowed uncontrollably down my face as I sat there alone in my bed. That creep from Acapulco's words came back to me in my solitude: "He kind of... hates you?"
I guess he was right, after all.
Setting aside the fact Lucy doesn't need to be tsundere about Zach in her internal monologue, this kind of stuff is okay and makes me like this more.
Anyway, this seems to be half agreeable and half horrible. I like the interpretation and the use of the narrator, but it doesn't reliably reflect Lucy's voice. It's either a boring "and then I did this, and then I did that, and I felt sad" kind of disconnected narrator, or one that reflect Lucy's fears and sadness and desperation in a way that makes it unreliable and harder to infer what is truly going on. I think you're struggling with the idea of faithfully following the sequence and dialogue from the comic, where this isn't necessary.
You should read the chapter, think about what you want to convey, and tell it differently. Don't try to imitate the comic. It's visual. This is prose, and it would benefit greatly from more creativity.