"If you have pain from a nerve and can't get rid of that pain, then you can't complete the rotation in your swimming, and you can't swim," Rene Tour told a press conference on Thursday.
"She is receiving treatment to reduce the swelling around the nerve and our physios are working full time.
"We are taking it one day at a time," he said, adding that Alshammar's condition was improving.
The 34-year-old Alshammar won the 50 metres freestyle at last year's world swimming championships in Shanghai and is still ranked inside the top eight in the world this year for the event.
Alshammar who also won two silver and one bronze medal at the 2000 Olympics in Sydney, has until next week to regain full fitness with the 100 freestyle heats not until Aug. 1 while the 50 freestyle heats are on August 3.
The swimming programme runs from July 28 until August 4.