Exposure to H2S can cause nausea, tearing and redness of eyes, with high levels of exposure causing dizziness, loss of appetite, fatigue and vomiting.
Emergency services flooded the school on Friday afternoon with more than 50 children suffering headaches, vomiting and skin irritation at South End School.
Police tracked down a plane originally believed to be involved in the incident and are "90 per cent sure" it didn't drop anything.
Barclay also ruled out the likelihood of a plane being involved, as it would be unlikely it could drop enough concentrated gas to the area.
She also quashed theories of fertiliser on school grounds being a potential source with it being dispersed in large areas.
"It's quite likely the source of something nearby and close to the ground than having something fly over.
"If you had a source that was close to the school it wouldn't necessarily need to be a very big source in order for the kids to be impacted by it," Barclay said.
The origin of the mystery substance could be tracked backwards if the meteorologist conditions were known at the time of the incident, she added.