What is the condition of the 19-year-old student with a painful belly button piercing?

The condition of the 19-year-old student with a painful belly button piercing is best understood as cellulitis. Cellulitis is a bacterial skin infection that manifests as redness, swelling, and pain in the area affected. In the context of a newly pierced belly button, such symptoms can arise from irritation or infection at the site, especially if proper care is not taken during the healing process.

When a piercing is new, the area is particularly vulnerable to bacteria, which can lead to infections like cellulitis. The pain experienced by the student, combined with potential redness and swelling around the belly button, aligns well with this diagnosis, as cellulitis often develops after bacteria breach the skin barrier, which is exactly what occurs with piercings.

The other conditions, such as cuts and bruises, an abscess, and allergic reactions, present differently. Cuts and bruises relate more typically to trauma rather than infection, an abscess would involve a pocket of pus and signs of a more severe infection, and an allergic reaction would typically involve rashes or redness that is more widespread or with other symptoms rather than localized pain and swelling. Thus, cellulitis is the most fitting diagnosis in this scenario.