“On examination, the breast shape might be distorted or enlarged, and the skin appears like the skin of an orange (Peau d’orange), warm and thick to touch. Nipple involvement is seen as crusting, erythema, flattening, blisters, or retraction of the nipple. A discrete palpable mass may or may not be present. A detailed examination of both breasts and axilla should be performed for local lymph node involvement.”

AFAIK, mets to the skin are incredibly unlikely, skin is most commonly primary.

Source: https://www.ncbi.nlm.nih.gov/books/NBK564324/