John Alagos, 24, became ill and died on Friday after working at Watford General Hospital in Hertfordshire.
His mother Gina Gustilo told the BBC the family were waiting to hear whether he had tested positive for Covid-19.
The hospital closed to new patients on Saturday due to problems with its oxygen equipment, but has now reopened. It said it ensured staff had the right level of protection when working.
Tracey Carter, chief nurse at the hospital, said: “John was very...