Final answer:
When a child sustains a contusion of the eye, the nurse should advise the mother to immediately apply a cold compress to the injured eye to help reduce swelling and minimize pain.
Step-by-step explanation:
In the case where a child has sustained a contusion of the eye, the most appropriate immediate response would be: a) Apply a cold compress to the injured eye. Applying a cold compress can help reduce swelling and minimize pain. Rubbing the eye (option b) is not recommended as it could exacerbate the injury. While over-the-counter pain medication (option c) might help with pain management, it should not be the first course of action without assessing the extent of the injury. Keeping the child lying down with the injured eye covered (option d) may help in some cases, but it is not as immediate a response as applying a cold compress.