Periorbital Cellulitis: This is the most likely diagnosis given the swelling under the eye after popping a pimple. Popping a pimple can introduce bacteria into the skin, leading to an infection. The proximity of the pimple to the eye and the act of popping it could have facilitated the spread of infection to the periorbital area.

Furuncle or Carbuncle: If the pimple that was popped was actually a furuncle (boil) or carbuncle, the infection could have spread locally, causing swelling and potentially leading to more serious infections if not properly managed.
Preseptal Cellulitis: Similar to periorbital cellulitis but limited to the area anterior to the orbital septum. It's a common complication of facial skin infections, including those resulting from popping pimples.
Erysipelas: A type of skin infection that can occur after minor trauma, including popping a pimple. It's characterized by a well-demarcated, erythematous, and edematous lesion.

Orbital Cellulitis: Although less likely than periorbital cellulitis due to the protective nature of the orbital septum, orbital cellulitis is a serious condition that can lead to vision loss, cavernous sinus thrombosis, and other severe complications if not promptly treated. It's crucial to distinguish it from preseptal cellulitis.
Cavernous Sinus Thrombosis: A rare but potentially life-threatening condition that can arise from facial infections, including those around the eyes. It requires immediate medical attention.

Necrotizing Fasciitis: A severe infection of the fascia, which could potentially occur after popping a pimple, especially if the patient has underlying conditions that predispose them to more severe infections. It's characterized by rapid progression and severe tissue destruction.
Lupus Miliaris Faciei: A rare, chronic condition that could be considered if the swelling and infection do not respond to typical treatments and there are other systemic symptoms. However, it's less likely given the acute presentation after popping a pimple.