What leads you to believe she had a serious accident?Who were her parents?
1911 Census 644/15 25/ 10 has her parents, John 59 and Elizabeth 57 and siblings, Marion 33, Andrew 26 at 77 Florence Street Glasgow. Elizabeth 20 is a Football Sewer. Married 35 yrs, 10 children of whom 5 are alive.
Sad story. Poor little Elizabeth She died in 1961 at this hospital https://en.wikipedia.org/wiki/Herdmanflat_HospitalShe died from a cororany thrombosis, aged 72. One of her brothers reported her death. James maybe from the names you mention for her sibings. See below.Like you, struggling to see her so far in 1901.
If your mother remembers visiting her in Morningside it may have been The Royal Edinburgh which was then and still is now a psychiatric hospital.The hospital Monica linked to was the same.I had a relative who died there aged 20 in 1936. I was able to call up and look at this medical notes as it was over 75 years since he had died. Reading them now I realise he died of sepsis but at the time it was obviously thought he had a delusional mental illness.I count my blessings for antibiotics!