Parapneumonic Effusion: Given the patient's recent treatment for an abscess with antibiotics, a parapneumonic effusion is a likely complication, especially if the abscess was pulmonary in origin. The presence of bilateral pleural effusion and edema supports this diagnosis, as it can occur as a result of the spread of infection to the pleural space.

Nephrotic Syndrome: This condition can cause edema and, in some cases, pleural effusions due to hypoalbuminemia. Although less directly related to the recent antibiotic treatment for an abscess, it remains a consideration in the differential diagnosis for bilateral pleural effusions and edema.
Congestive Heart Failure (CHF): CHF can lead to both bilateral pleural effusions and peripheral edema due to fluid overload. The recent history of an abscess and antibiotic treatment is not directly related, but CHF should be considered, especially if there are underlying cardiac issues.
Systemic Lupus Erythematosus (SLE): SLE is a systemic autoimmune disease that can cause pleural effusions and edema among its myriad manifestations. It is more common in young females and could be considered, especially if other systemic symptoms are present.

Pulmonary Embolism (PE): Although less likely given the context, PE can cause pleural effusions and should not be missed due to its high mortality rate if untreated. The presence of edema could also be related to deep vein thrombosis (DVT), a common source of PE.
Sepsis: If the patient's abscess was not fully resolved or if there is another source of infection, sepsis could lead to both pleural effusions and edema. Sepsis is a medical emergency and must be promptly recognized and treated.

Lymphangioleiomyomatosis (LAM): A rare lung disease that primarily affects women of childbearing age, LAM can cause pleural effusions. It is much less common and would be considered if other diagnoses are ruled out and there are characteristic findings on imaging.
Eosinophilic Granuloma with Polyangiitis (Churg-Strauss Syndrome): This is a rare autoimmune condition that can cause asthma, eosinophilia, and vasculitis, potentially leading to pleural effusions and edema. It would be considered with a history of asthma and eosinophilia.
Yellow Nail Syndrome: A rare condition characterized by yellow nails, lymphedema, and pleural effusions. It is very rare and would be a diagnosis of exclusion.