I often sent DS to school if he had vomitted once before school because he regularly vomitted because of stress and anxiety, quite often in the morning or before a big event. 90% of the time I was right and he was absolutley fine but occasionally - two times in his primary school career,- it was an indication that he was ill and he vomitted again at school and came home as he was ill.
Both times I got an earful from the school because DS told them he had vomitted at home in the morning (of course he bloody had, he did at least once a week every week during term time especially)
I just smiled, apologised and ignored the telling off it because if I had kept DS off every time he vomitted once he would have had much lower attendance than he already had . We were already being hassled about t his attendance
So yes on a couple of occasions I made the worng call to send him to school after vomitting but I can't be sorry about that because I had very little choice and since I had to make that call 1-2 a week for about 6 years, I had a pretty good success rate at being right that the vomitting was anxiety not illness
Of course the vomitting from anxiety was its own issue but far more complicated to deal with than just deciding if he should go to school or not . We cancelled of his 2 birthday parties because he vomitted the night before, when in fact he was fine but we had the choice and I didn't want to be wrong and have a lot of children's parents be annoyed with me.
I remember making another call when he went to a friend's house for a play date and was sick just before we left then being called as he had vomitted at the friend's house a second time - I lost that friend as no explaining the issue could convince her I wasn't being very selfish
We cancelled a holiday twice both times because as I didn't want to take him on a plane as I was not sure if hs vomitting was illness or anxiety. In fact it was illness one time so I made the right call that time but anxiety the other - so sometimes I got it right and sometimes (less often) I didn't - so sue me