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Waking up vomiting (once) at night .. fine during day... school or not?
We had this about two years ago with DD. Went on for about four days before I took her to the doc. Same symptoms as your DS - only vomiting at night after a bit of a cough. Fine in the day. A short course of antibiotics killed it off. While in Australia recently we had it again, and because of where we were and the fact that she was fine in the day, we didn't seek medical help, and it went on for three weeks before she managed to get through it. I know that's not exactly a randomised controlled trial, but it might be worth getting some antibiotics?
Is he eating properly ? dd throws up when she has a cough, we keep her pillow end of mattress permanently elevated to try to prevent it. If he isn't unwell and is eating and drinking normally then send him but if he is off food and not himself keep him off for 24 hours after last sick incident.