Final answer:
For a child stung by a wasp without anaphylaxis, the nurse should recommend over-the-counter benzocaine, a local anesthetic that can be applied topically to relieve pain.
Step-by-step explanation:
If a child has been stung by a wasp and is in pain but shows no evidence of systemic effects or anaphylaxis, the nurse should recommend an over-the-counter local anesthetic to relieve the child's pain that is meant for topical use rather than injection.
Among the options provided, benzocaine is an appropriate choice as it is available over-the-counter and can be applied topically to alleviate pain from insect stings. It is important to note that drugs like bupivacaine, mepivacaine, and chloroprocaine are typically used for more invasive procedures and would not be appropriate for over-the-counter use for a wasp sting. Therefore, the correct answer is D. benzocaine.