I could be wrong but I think Ancestry have a collection of WW1 Nurses documents. Might be worth looking at the National Archive collection also. Could you post your grandmothers details (date of birth etc) and I could check Ancestry for you later? All the best
If she was a member of the Royal College of Nurses, they may be able to help: https://www.rcn.org.uk/development/rcn_archives/research_advice_-_tracing_nurses However, as you say she was a Red Cross nurse, she would probably be classified as a VAD. See this page on the RCN site: Military nursing records - RCN The National Archives records only cover army nurses: British Army nurses' service records 1914-1918 | The National Archives Find My Past has some military nursing records as well, but they seem to duplicate TNA: Military Nurses 1856-1940 records published on findmypast.co.uk
