Final answer:
The nurse should recommend the application of a warm compress for non-pharmacological pain management in a breastfeeding client experiencing engorgement.
Step-by-step explanation:
The nurse should recommend the application of a warm compress for non-pharmacological pain management in a breastfeeding client experiencing engorgement. Engorgement is the overfilling of milk ducts in the breast, leading to discomfort and pain. Applying a warm compress can help to relieve the engorgement by promoting blood flow and reducing inflammation. It can also soothe the breast and provide a sense of comfort.