Furuncle (Boil): A furuncle is a deep-seated infection of the hair follicle, typically caused by Staphylococcus aureus. The description of a nickel-size pimple with a pinpoint opening at the center, which appeared after popping, is consistent with a boil. The absence of significant pain or drainage also aligns with this diagnosis, as not all boils are severely painful or draining.

Infected Epidermal Inclusion Cyst: These cysts can become infected, leading to symptoms similar to a boil, including redness, swelling, and sometimes a pinpoint opening if the cyst ruptures. The mild itch and absence of severe pain or drainage could fit this diagnosis.
Folliculitis: An infection of the hair follicles, which can present with redness, swelling, and sometimes pus. The location under the breast, where friction and moisture can be higher, makes this a plausible diagnosis.
Abscess: Although the patient denies drainage, an abscess could present similarly, especially if it's not fully developed or if the drainage is minimal. The presence of an abscess would typically be accompanied by more significant pain, but this can vary.

Breast Cancer with Secondary Infection: Although rare, any new skin lesion or change in the breast area warrants consideration of breast cancer, especially if there's an associated infection. The presence of a "pimple" that doesn't resolve or changes over time could be a sign of an underlying malignancy.
Necrotizing Soft Tissue Infection: This is a severe infection that can start with minimal symptoms but rapidly progresses. The absence of severe pain or significant drainage does not rule out this diagnosis, as it can present subtly at first.

Hidradenitis Suppurativa: A chronic skin condition characterized by recurrent, painful abscesses and nodules in areas of the body with apocrine sweat glands, such as the underarms or under the breasts. The description provided doesn't fully align with the typical presentation of hidradenitis suppurativa, but it could be considered if the lesion is recurrent or part of a larger pattern.
Cutaneous Metastasis: Metastatic disease to the skin from another primary cancer site. This would be an extremely rare presentation but should be considered in the differential diagnosis, especially if there's a known history of cancer.