Nephrotic Syndrome: This condition is characterized by heavy proteinuria (excess protein in the urine), hypoalbuminemia (low albumin in the blood), and often edema. The presence of 3+ protein in the urine along with low total protein and albumin in the blood strongly suggests nephrotic syndrome, which can be caused by various conditions including minimal change disease, focal segmental glomerulosclerosis, and membranous nephropathy.

Viral Glomerulonephritis: Certain viral infections can cause inflammation of the glomeruli, leading to proteinuria and changes in blood protein levels. The viral syndrome presentation could be related to the underlying cause of the glomerulonephritis.
Hepatic Cirrhosis with Nephrotic Syndrome: Liver disease can lead to both hypoalbuminemia and proteinuria due to secondary effects on the kidneys or due to a hepatorenal syndrome. The viral syndrome could be indicative of a viral hepatitis.
Protein-Losing Enteropathy: Although less likely given the specific combination of findings, this condition involves the loss of protein through the gastrointestinal tract, which could potentially lead to hypoalbuminemia. However, the significant proteinuria would need another explanation.

HIV-Associated Nephropathy (HIVAN): HIVAN can present with significant proteinuria and renal dysfunction. Given the viral syndrome, HIV testing is crucial as HIVAN is a potentially treatable condition that could explain the renal findings.
Systemic Lupus Erythematosus (SLE): SLE can cause renal involvement (lupus nephritis), leading to proteinuria and changes in blood protein levels. The diagnosis of SLE is critical due to its potential for significant morbidity and the availability of specific treatments.
Amyloidosis: This condition involves the deposition of amyloid proteins in various tissues, including the kidneys, leading to proteinuria and renal dysfunction. It's a diagnosis that would significantly alter management and prognosis.

Lymphoma: Certain types of lymphoma can cause renal involvement, leading to proteinuria. While rare, lymphoma is a diagnosis that would have a significant impact on treatment and prognosis.
Monoclonal Gammopathy of Renal Significance: This condition involves the production of abnormal proteins that can damage the kidneys, leading to proteinuria. It's a rare diagnosis but one that could explain the combination of findings in the context of a viral syndrome, potentially related to a paraproteinemia.