Karen McNeil had been trying on clothes in Quiz, at The Forge in Parkhead, when the alarm went off.
But distracted by daughter, Mollie, the 31-year-old did not hear the alert sound.
When she came out of the changing room the shop was deserted, the barriers down and the city shopping centre was being evacuated.
Karen said: "I was shaking from head to toe and didn't know what to do, I felt physically sick and couldn't think straight.
"Mollie had been singing and dancing and we didn't hear the alarm.
"When I came out of the changing room the shop was deserted. I'm not even sure how long the alarm had been sounding for."
Karen started searching for the number of The Forge on her smart phone and rang the main office three times but no-one answered.
She said: "I saw a window and started chapping it to try and get the attention of the people who were leaving the centre. Luckily two women saw me and one went to look for help."
Eventually, a worker from a neighbouring shop came to her rescue.
Karen added: "A girl from the shop next door came back into the building to help me. Just a few moments later the manager of Quiz appeared.
"I told her what had happened and she sort of laughed a nervous laugh and asked where I'd been.
"I said that my four-year-old daughter and I had been in the changing rooms and no-one had come to check on us."
The manager then offered Karen a discount on a dress.
But the childcare worker refused the offer.
She said: "I don't want this to be swept under the carpet. I have contacted the Quiz head office and heard nothing in reply.
"A discount off a dress is not really a fair response. If there had been a fire then Mollie and I could have died.
"I tried not to let Mollie see that I was scared, but she must have picked up on the situation."
A spokesman for Quiz said: "I was sorry to learn of the experience of the customer being locked in store during the fire drill.
"We at Quiz take our health and safety obligations very seriously and this was an oversight by our store manager.
"While we do have comprehensive procedures in place for these situations, we will ensure these are refreshed with the store team.
"We have since spoken to the customer and offered her the opportunity to pick a new outfit on us, along with a full apology."
A spokesman for the Scottish Fire and Rescue Service confirmed three appliances attended a false alarm at 11.18am on Friday.
Paul Wishart, centre manager for The Forge, said numerous practice fire drills are held at the mall.
He added: "We have very clear procedures in place and in this instance they were not followed by the individual shop."