Laura Plummer, 33, a shop worker from Hull, was arrested as she entered the country in the Red Sea resort of Hurghada carrying 320 tramadol tablets in her suitcase.
Her family said they were for her Egyptian partner, Omar Caboo, who suffers from severe back pain and claimed Ms Plummer, who they describe as “daft”, had no idea what she was doing was illegal.
Tramadol, a painkiller, is a class C drug that is banned in Egypt but legal in the UK.
However, it is only available when prescribed by a doctor or other healthcare professional and it is illegal for anyone else to supply it.
Laura’s sister, Rachel, said her mother, Roberta Synclair, who travelled to Egypt for the hearings, was distraught over the sentence.
She said: “My mum’s obviously devastated. She’s out there by herself.”
The family have lodged an immediate appeal, but Rachel said she did not know whether it would be heard on Tuesday.
She said: “We’re just hoping. Even half of that would be better. Anything less than three years. She doesn’t deserve that.”
The family said Ms Plummer made no attempt to hide the medicine, which she was given by a friend, when she was searched by customs officials as she arrived for a holiday with her partner on 9 October.
Ms Plummer appeared in court on Christmas Day, but the case was adjourned due to the condition she was in, according to her sister, who described her as “sleep deprived”, “visibly nervous” and “upset”.
A Facebook group set up by her family announced that she appeared in court on Boxing Day and was jailed for three years.
Mrs Synclair said her daughter was sharing a communal cell with no beds with up to 25 other women in the Red Sea resort of Hurghada, where she was arrested at the airport.
Her family had been told that she could face up to 25 years in jail, with one lawyer even mentioning the death penalty.
Ms Plummer’s local MP, Karl Turner, admitted the result could have been much worse, but still described it as “devastating”.
He told Sky News: “She’s been very anxious, she’s suffered sleep deprivation, she’s not been well in terms of her mental health and her physical health.”
Mr Turner also urged Egyptian authorities to “think very hard about what this means to people in the UK who are considering travelling (there)”.
And of the police cell where Ms Plummer was being held, he said: “Frankly, for anyone the conditions would be shocking but for a young woman who has never so much as committed a parking violation, this experience will be utterly shocking to her.”
The Hull East MP added: “I’ve got a lot of confidence in the British Foreign Office. I think they’ve dealt with this case particularly well.
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“Boris Johnson has himself taken a particular interest in this case and had meetings with Government ministers about it. I’m hoping that good sense and decency will prevail.”
A Foreign Office spokesman said: “We will continue to provide assistance to Laura and her family following the court ruling in Egypt, and our embassy is in regular contact with the Egyptian authorities.”