I Gave My 4 Year Old A Half Dose Of

I gave my 4 year old a half dose of benadryl for her allergies and sinuses and she wantes to use the dropper but she squeezed it hard and when it hit the back of her throat she bagan to cough hard and threw up a little. She is no longer coughing hard but a little here and there. Could it have got into her lungs and will she be ok? It was approximately 1/2 teaspoon.