Actually,
Spoiler:
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The MC and his sunbae from the real world were truly caught up in the building collapse. The lil sis too, she's the lil bro in this world like you said and sunbae is ML. Both died in the collapse already but MC is still dying.
The time lapse is different in both worlds and that's why MC gets sick here. As a side effect of him feeling himself dying in the other world.

Anyone else is reminded of Cozy Obsession? The plot is giving me the same kind of headache and anticipation, i cant wait for the plot to unfold