I think Allisgood is getting a bit of a hard time here.
I am a trained nurse, and ds2 broke his wrist on a Saturday lunchtime, but we didn't realise how serious the injury was until 24 hours later, when he couldn't put his weight on it - up to then, he'd been a bit sore (relieved by calpol) and able to play football, and had slept fine - it took an x-ray to diagnose.
And she has said she didn't send her child in with a dental abcess - that developed later - her child had had a filling, been sore afterwards (not unexpected, imo) but that soreness had been relieved by calpol - so she assumed, as I would, that it was just post-filling soreness, and sent her in to school, expecting that if her dd was in pain later on, she'd be notified.
In the third example, her child did not have a temperature when she sent her in - it developed during the day - to the point where the school nurse took her temperature and recommended she be sent home - and the school did not send her home - how is that OK?
Schools are full of adults who are just as capable as a mum of judging a child's condition - plenty of us have been phoned by our children's schools to fetch them home when they become unwell during the day. No parent has a crystal ball - we all make the best judgements we can, with the information we have at the time. In each of these examples, the OP thought she was making the right decision to send her child to school - had she had x-ray vision, or the power of foresight, and had known the wrist was broken, an abcess was going to develop, or her dd's temperature was going to rise dramatically from normal - of course she would have kept her at home.
But she didn't - so she sent her child in, and trusted that, if her condition changed, and she was not well enough for school, she would be sent home - and that is not unreasonable, IMO.
If a child vomits at lunchtime, should the school keep them there, because they were OK when the parents sent them in? Of course not - they should send them home. Same would apply if a child had an injury at school - as ds2 did when he broke the other wrist playing football - the school rang us to take him to A&E. They didn't keep him in school because his wrist hadn't been broken when he arrived there that day!
Yes, with the power of hindsight, the OP shouldn't have sent her child in - but no-one has hindsight BEFORE the event - that is why it is called hindsight. Her dd's condition worsened each time, during the school day, and the school did not contact her.