Looking at his medical record he did suffer a gun shot wound to his head and face, but it's unclear when he received the GSW as it isn't mentioned until 26/11, but as that was also the day he was shipped back to England on the hospital ship Brighton from 26 Gen Hospital Etaples, which was a base hospital in France, I doubt he received it on the 26th.
In my mind and reading between the lines he probably received the GSW and was taken to 2 CCS (Casualty Clearing Station) on the 7/11 with concussion and being dangerously ill.
On the 10/11 he was transferred from 2 CCS to a base hospital, and on the 11/11 he was diagnosed with an accidental severe fractured skull and was admitted to 26 General Hospital, Etaples. Then on the 26/11 when he arrived in England from Etaples he was admitted to the Special Military Surgical Hospital Edmonton (now the North Middlesex Hospital) where it was discovered he had a GSW head and face, which was the cause of his fractured skull.
Hope this makes sense to you and apologies if I'm miles out.