子どもが夜中に咳こみながら嘔吐あせる

My child threw up with coughing at night.

熱は微熱程度だし、本人は元気だけど、悪化しないよう幼稚園は休ませることに

Although my child has a slight fever, he is so fine.
However so fine, I keep him home so that he won't get worse.

最近イベント続きで疲れたまっちゃったかな~ショック
He might have been exhausted lately, because we had many events.

#最後の「疲れがたまる」とか、調べながらの英訳なので、表現がちょっと自信ないな~