The speaker is in pain and working hard to keep it hidden. On the surface she smiles and laughs at what someone says, but her body tells a different story: her skin crawls, and there is blood under her fingernails. She knows the face in front of her, yet the hands don't feel safe. She says she has told this person about "that fight," though the poem never spells out what happened. Judging by the imagery, it was something that left her feeling violated or unclean.
The second stanza turns to self-punishment. She cuts off her hair to erase "that girl" and burns away what she can't bear in her own skin. The parenthetical lines read like private thoughts breaking in, and they trace a fall: an angel with burning wings drops from the sky, and the speaker's own sky falls with her. The mood is raw, numb and desperate, caught between shame and a wish to disappear.