Sjögren's Syndrome: An autoimmune disorder that often presents with bilateral parotid gland swelling, among other symptoms like dry eyes and mouth. The recurrence of swelling after antibiotic treatment (Bactrim) suggests a non-bacterial cause, making Sjögren's Syndrome a plausible diagnosis.

Sialadenitis (Recurrent): Although the patient has been treated with antibiotics (Bactrim) twice, the possibility of recurrent bacterial sialadenitis cannot be entirely ruled out, especially if the cause is a blockage or stone that hasn't been addressed.
HIV-Associated Parotid Gland Enlargement: HIV infection can cause parotid gland swelling, often bilateral, as part of the diffuse infiltrative lymphocytosis syndrome (DILS). Given the patient's age and the lack of response to antibiotics, HIV testing might be warranted.
Lymphoma: Both Hodgkin's and non-Hodgkin's lymphoma can involve the parotid glands, though this is less common. The swelling could be part of systemic lymphadenopathy.

Sarcoidosis: A systemic granulomatous disease that can affect any organ, including the parotid glands. It's crucial to consider sarcoidosis due to its potential for serious complications if left untreated.
Tuberculosis: Although rare in the parotid glands, tuberculosis can cause swelling and is a critical diagnosis not to miss due to its public health implications and the need for specific treatment.
Parotid Gland Tumors: Both benign and malignant tumors can cause swelling. While less likely to be bilateral, the possibility of a tumor, especially in the context of recurrent swelling, necessitates further investigation.

Heerfordt's Syndrome: A variant of sarcoidosis that specifically involves the parotid gland, uveitis, fever, and cranial nerve paralysis. It's rare but should be considered in the differential due to its unique presentation.
IgG4-Related Disease: A systemic fibroinflammatory disease that can affect the parotid glands among other organs, leading to swelling. It's a rare condition but one that requires specific treatment.
Eosinophilic Sialadenitis: A rare condition characterized by eosinophilic infiltration of the salivary glands, which can cause swelling. It might be associated with other systemic conditions like eosinophilia or allergic reactions.