Best thing for gastroenteritis type probs is water, lots of it, small amounts frequently (if it is down for 15 mins they've got it in their system) adding up to about 200ml per hour (whilst awake). Very dilute low sugar squash does well too and is a bit less boring than water, but avoid sugary drinks or caffeinated drinks, as the latter can make you pee out more than you take in. Food should be avoided for 24 hours, reason being that the bowel is usually inflamed, so giving it a natural rest is a good thing, whilst the fluids avoid dehydration. Any bugs are then shed naturally. The mistake which most people make is to start eating too early, usually at the first signs of hunger, so the bowel doesn't settle and the diarrhoea continues. Loperamide and similar really should be avoided even if the diarrhoea is very frequent and profuse, as it can slow down the overall recovery. If however the diarrhoea continues unabated for 2-3 days despite fluids only sometimes it is necessary to use it. Antibiotics have no place in treating most of these conditions and can make the diarrhoea worse in certain instances. As most gastroenteritis is over by and large within 24-72 hours neither a medical consultation, medication or tests are usually necessary. There are always exceptions of course, including infants and very small children, who are more vulnerable to dehydration and can uncommonly get quite poorly.
As for seeing a Dr every time a child is off school, that is a nonsense in any country and should be resisted. In my experience parents are usually best judge. The GPs have got plenty to do without as idun says, seeing minor ailments clutter up their surgeries, 23 euros or not. If it isn't a legal requirement, don't do it. Tell the school by all means, but just get your child back to school as soon as you think they can tolerate it.