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.
According to a Facebook group set up by her family, she appeared in court in Egypt on Boxing Day and was jailed for three years.
The family said her lawyers lodged an immediate appeal.
Ms Plummer appeared in court on Christmas Day, but the judge adjourned the case for a day because of her condition, according to her sister, Rachel.
Their mother, Roberta Sinclair, travelled to Egypt for the hearings.
The Plummer family has previously said Ms Plummer 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.
Ms Sinclair said her daughter was being held in terrible conditions in a communal cell with no beds, sharing with up to 25 other women.
Ms Plummer is being held in the Red Sea resort of Hurghada, where she was arrested at the airport on 9 October.
Her family had been told she could face up to 25 years in jail, with one lawyer even mentioning the death penalty.
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