Cellulitis: This is a common skin infection that can start as a small, red area and expand over time. The fact that it was initially thought to be a bug bite and then expanded, along with the lack of response to antibiotics, could suggest a more complex infection or an incorrect initial diagnosis. However, cellulitis is often the first consideration for such presentations.

Erysipelas: A type of skin infection that involves the upper dermis, typically caused by beta-hemolytic group A Streptococcus. It presents as a well-demarcated, red, and painful lesion, which could fit the expanding red area description.
Contact Dermatitis: An allergic or irritant reaction to something that came into contact with the skin, which could have been mistaken for a bug bite initially. The lack of response to antibiotics would support this diagnosis, as contact dermatitis does not respond to antibiotics.
Impetigo: A contagious skin infection that can cause red sores on the skin, which could have started from a bug bite. However, it typically responds to antibiotics, so the lack of response might make this less likely.

Necrotizing Fasciitis: A severe infection that destroys the tissue under the skin, including fat and the tissue covering the muscles (fascia). It's a medical emergency and can start from a minor injury or infection. The expanding red area and lack of response to antibiotics could be indicative of this condition, especially if there's significant pain out of proportion to the appearance.
Breast Cancer with Infection or Inflammatory Component: In rare cases, breast cancer can present with skin changes that mimic an infection, including redness and swelling. This would be particularly concerning in a postmenopausal woman.
Lymphangitis: An infection of the lymphatic vessels, which can cause red streaks that move up the arm or leg. While less common in the breast area, it's a possibility if the initial "bug bite" was actually an entry point for infection.

Erythema Migrans (Lyme Disease): Although typically associated with a distinctive "bull's-eye" rash, erythema migrans can sometimes present as a solid red patch. Given the initial thought of a bug bite, if the patient is in an area endemic for Lyme disease, this could be considered.
Sweet Syndrome (Acute Febrile Neutrophilic Dermatosis): Characterized by the sudden onset of fever, leukocytosis, and tender, erythematous, well-demarcated papules and plaques. It's rare and could be considered if other diagnoses are ruled out and the patient has systemic symptoms.