I do give my two SW CAH boys a shot whenever they vomit from illness.  I have never taken them to the hospital by way of car or amulance for an illness.  They have had stitches and a few minor broken bones.  In my humble opinion you did overreact,  but you do learn from each experience and every child is different, and you will have a better idea what to do next time. My kids are 5 and 8 years old.

 

Good luck to you.