No, ordinary charcoal won't work. You need activated charcoal for medicinal purposes.
A chicken has one crop, located on the right side of the chest. In the throat, on the far right side is the esophagus and it leads directly into the crop. The hole in the center is the airway or larynx. Anything you put into a chicken's throat must be kept clear of that hole or the chicken will choke, same as if you get something in your airway.
You need to go to the store where they sell people vitamins. You will find activated charcoal there. It comes in capsules. Break one open and mix it with water and syringe that charcoal and water mixture into the crop as shown in the photo. Adding a little sugar to the mix will help keep the chick from going into shock.
Too much time may have lapsed already to save this chick if it is indeed suffering from toxin ingestion. If it's something else, the chick might survive if you figure out what's wrong and can treat it.
Heat sickness is another possibility. The symptoms are very similar to toxin poisoning. If it's been very hot where you live, you might treat for dehydration and hyperthermia. To do that, give electrolytes containing sugar and cool the chick with cool compresses under the wings.