When treating a patient who has consumed a corrosive poison, it is crucial to avoid any actions that could exacerbate the damage to the throat and esophagus. The patient's throat is already swollen, indicating inflammation and potential injury to the mucosal lining. Giving the patient soothing drinks can help to coat and protect the mucous membranes, providing some relief from pain and irritation. These drinks can also help to dilute the corrosive substance, reducing its harmful effects.

**_ Inducing vomiting is not recommended in cases of corrosive poisoning. Vomiting can cause the corrosive substance to come into contact with the esophagus and oral cavity again, leading to further injury and potential complications such as aspiration. Hot liquids can increase irritation and inflammation of the already damaged mucosal lining in the throat and esophagus. It is important to provide soothing and neutral temperature liquids to avoid exacerbating the injury. While applying a cold compress might provide some external relief, it does not address the internal damage caused by the corrosive poison. The focus should be on minimizing further harm to the internal tissues. Among the given options, giving soothing drinks is the most appropriate measure for a patient who has consumed a corrosive poison and has a swollen throat. It helps to provide relief and minimize further damage to the mucosal lining, while other options could potentially cause additional harm or fail to address the internal injury.