Dorrance said she burst into tears when she sat down and had to leave. She described the experience as "awful" and "humiliating".
The capital has this week hosted the Youth Parliament, which every three years brings together teenagers from around the country to try their hand at being MPs, including by speaking in the House, in front of cameras.
Other students had earlier debated with Tolley about "reading", after being given similar warnings, despite earlier being told to bring written notes.
In a statement, Tolley said she felt "terrible".
"I'm so sorry if I upset anyone and certainly apologised to a couple of people," she said.
"I was trying to get them to speak 'from' their notes rather than just 'read' them in the general debate which, as you know, is a robust debate in Parliament."