I'm sorry. I should have given you better instruction.
View attachment 2657745The esophagus is an open channel on the chicken's right side of their throat. With baby chicks, you either use a slender syringe or eye dropper and slide it to the back of the right side of the throat, or just give a drop at a time in the right side of the beak. If you squirt it into the mouth without keeping to the side of the mouth, the fluid can go into that center hole you can see behind the tongue, and that is the airway leading to the lungs. Often, a little fluid may make a chicken cough, and then you know you're squirting it too far toward the center and you then need to reposition the syringe so it's along the side of the throat as shown here.
But I still have doubts you caused the chick to aspirate. Usually it kills the chicken instantly.
Please try not to feel that you did something to cause this death. And even if you did, we all can't know everything about chickens all the time and do exactly the correct thing. I've lost more than my share of chickens because I didn't know what I was doing. About the only people who have never lost a chicken to a human mistake are those that have just returned home with their very first chicks.