Khadija Shah, 25, has been held in custody with her daughter, aged four, and her five-year-old son.
She says she had been on holiday in Pakistan with relatives and had no idea what was in the cases.
The BBC's Orla Guerin said if Miss Shah was convicted she could face the death penalty.
Miss Shah, who has not been formally charged, said some men asked her to take the bags to the UK as a favour.
Miss Shah was accused, at the court in Rawalpindi, of trying to smuggle 63 kilos of heroin.
She said if Miss Shah was convicted she could face the death penalty.
Miss Shah, who was six months pregnant, was arrested in Islamabad in May as she tried to board a flight back to Birmingham with her children.
Miss Shah told the BBC: "I had no idea what was in them. I wouldn't do that with two young children".
She told our correspondent conditions in prison were absolutely horrific, with stifling heat and overcrowded cells.
The legal charity Reprieve says Miss Shah's children contracted measles in jail, and claims other pregnant women have died in the prison where she is being held.
Reprieve said Miss Shah could not understand the legal proceedings against her as she did not speak Urdu.
She is due back in court on 29 June, when she is expected to be formally charged.
A pregnant woman from Birmingham has appeared in court in Pakistan after being arrested last month with heroin worth £3.2m in several suitcases.