Shop worker Laura Plummer, 33, from Hull, was arrested after she was found to be carrying 290 tramadol tablets in her suitcase, a painkiller which is legal in the UK but which is banned in Egypt.
Ms Plummer's family, who have described her as "naive", said she was taking the tablets for her Egyptian partner Omar Caboo, who suffers from severe back pain.
Her mother Roberta Sinclair travelled to Egypt for the Christmas Day hearing.
Her sister Rachel Plummer said the judge adjourned the case for a day because of Laura's condition.
She said: "She's sleep deprived, she's visibly nervous and upset.
"She's answered some questions wrong because she's not understanding them, she obviously can't think straight.
"You can imagine the pressure - this is her life."
She said their mother and Mr Caboo were denied access to the hearing as their driver took them to court late.
Meanwhile, the Hull East MP Karl Turner has praised the Government and Foreign Secretary Boris Johnson's efforts for the Plummers.
The Labour MP said Foreign Minister Alistair Burt had been to Egypt and spoken to his counterparts.
He said: "I don't think we could have asked for any more.
"Unfortunately ministers can only do so much, the judiciary in Egypt is independent and impartial and the judge will come to a view without any outside influence."
Mr Turner said: "The evidence is pretty clear that she didn't know the drug was banned and she was taking it out there to help her boyfriend, who has come up with the evidence that he does suffer from a severe back problem.
"The lawyer acting for them is very honest and has said the situation is very serious.
"But there is an awful lot of good things to say on behalf of Laura, and hopefully the judge will use his or her discretion."
The Plummer family has previously said she had no idea that what she doing was illegal and was just "daft".
They said she did not try to hide the medicine, which she had been given by a friend, and she thought it was a joke when she was pulled over by officials after arriving for a holiday with her partner.
Mrs Sinclair said her daughter was being held in terrible conditions in a communal cell with no beds, sharing with up to 25 other women.
She said she looked "unrecognisable".
Ms Plummer is being held in the Red Sea resort of Hurghada, where she was arrested at the airport on October 9.
Her family has been told that she could face up to 25 years in jail, with one lawyer even mentioning the death penalty.