Update 20:30: Stella came back home again about half an hour ago.
She was a bit wobbly and said her circulation was still iffy, and the doctors would have preferred to keep her there overnight, but she signed a waiver and took a taxi home. (She told Amy it's because she didn't want her to be alone.) She had something to eat and wants to see how she feels then.
She's cuddling in Amy's bed with her right now.
She said the doctors suggested she get an emergency packet to keep with her in case something similar happens in the future (presumably with an epi-pen or something similar).
20:45: She said that after she had eaten the peanut thing, her tongue felt as if it had swollen up. She tried drinking some water and brushing her teeth to see whether that would make it go away, but it didn't. And when her knees started feeling wobbly, she went upstairs to the neighbours.
They called the ambulance, and the medics(?) took her blood pressure and said they'd prefer to take her to hospital, where she spent a while on a gurney until a doctor had time for her.
An ENT doctor looked at her throat but couldn't see anything out of the ordinary. They gave her some cortisone and something else and said they'd be back a bit later. When they came back to check up on her, she said that she didn't feel any different, and they said they'd like to keep her overnight.
She said her throat felt fine again and it was just her circulation which was still down, and the doctor said she could go home if she insisted but only if she signed the waiver, which she did.
She's still wobbly and has now gone to bed. But the worst seems to be over. And she'll see a doctor about getting an epi-pen or whatever so the next time will, hopefully, not be as frightening.
Thank you all for your thoughts.