Just seen your message for the first time. There were two military hospitals during WWII in Malta - Bighi Hospital in Kalkara (Cottonera Area) and Mtarfa Hospital near the old citadel MDINA. There were also two other hospitals - one in Floriana and The Blue Sisters Hospital in St Julians run by the nuns. If your ancestor was in the services try and find information from UK National Archives since all files were sent there after the British left the Island.
Good Luck
Carmen Rossiter