Plummers sister Rachel said her mother Roberta Sinclair was "devastated" by the sentence, the report said.
They have claimed she is being held in a small cell in Hurghada in repulsive conditions.
She said he daughter has been "living in hell" sharing a jail cell with no beds with up to 25 other women, adding her daughter now looks "unrecognisable".
Her lawyer said Plummer would appeal, seeking to reverse the verdict or get a commuted sentence, which is possible in the two months after being sentenced. She will probably be dead if she has to stay in there for three years.
"My mum's in pieces, Laura is in pieces".
The 33-year-old woman from Hull has maintained her innocence since her arrest, insisting that the Tramadol tablets were for her Egyptian partner who suffers from chronic back pain.
However, as a class C drug, 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 mum, Roberta Sinclair, says her daughter made no attempt to hide the medicine and thought it was a joke when she was first pulled over by officials.
On Monday the lawyer, Mohamed Othman, told Reuters: "It is illogical that she was dealing in Tramadol".
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".
Ms Synclair added: "It's affected all our lives".
"She's a normal, nice person".
Her legal team are to put in a bail application that could see Laura freed from the detention centre where she has been since October 9.
A spokesman from Britain's Foreign and Commonwealth Office 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".