First time mothers have a lot of time to get home and have a meal, rest, and start timing the contractions. The first contraction, or often the first 100 contractions, rarely elicits an exclamation from the mother. They start out very gradually, becoming more frequent and more intense as the hours go by. Indeed, if the first few contractions caused that much discomfort, I would encourage a mother to go to the hospital as this would be unusual. My advice is to try not to worry about this scenario.
Most people are very kind, and actually excited, when they hear someone is in labor.
And the likelihood of hard labor starting at school is very remote. I hope this has helped ease your mind. I wish you a great experience and a healthy and happy baby. Watch kids controlling behavior of breath holding. Most children do not get enough water in their diet.