Rheumatoid Arthritis (RA): This is the most likely diagnosis given the insidious onset of multiple joint pain and swelling, along with high inflammatory markers. RA is a chronic autoimmune disorder characterized by symmetric polyarthritis, and the presence of high inflammatory markers such as ESR and CRP supports this diagnosis. Although high bilirubin and nausea/vomiting are not typical presentations of RA, they could be related to medication side effects or other comorbid conditions.

Systemic Lupus Erythematosus (SLE): SLE is another autoimmune disease that can present with multiple joint pain and swelling, along with high inflammatory markers. The presence of high bilirubin could indicate liver involvement, and nausea/vomiting could be related to gastrointestinal or central nervous system involvement.
Seronegative Spondyloarthropathies: This group of diseases, including ankylosing spondylitis, psoriatic arthritis, and reactive arthritis, can present with multiple joint pain and swelling, along with high inflammatory markers. However, they typically have a more asymmetric distribution and may be associated with other symptoms such as back pain or skin rashes.
Septic Arthritis: Although less likely given the insidious onset, septic arthritis can present with multiple joint pain and swelling, along with high inflammatory markers. The presence of high bilirubin and nausea/vomiting could indicate a systemic infection.

Hemochromatosis: This genetic disorder can lead to iron overload, causing joint pain and swelling, along with liver dysfunction (high bilirubin) and gastrointestinal symptoms (nausea/vomiting). Although rare, it is a potentially treatable condition that should not be missed.
Lymphoma: Certain types of lymphoma, such as Hodgkin lymphoma, can present with systemic symptoms including joint pain and swelling, along with high inflammatory markers and liver dysfunction.
Sickle Cell Disease: This genetic disorder can cause vaso-occlusive crises, leading to joint pain and swelling, along with liver dysfunction and gastrointestinal symptoms.

Relapsing Polychondritis: This rare autoimmune disease can cause cartilage inflammation, leading to joint pain and swelling, along with high inflammatory markers. The presence of high bilirubin and nausea/vomiting could indicate other systemic involvement.
Whipple's Disease: This rare bacterial infection can cause systemic symptoms including joint pain and swelling, along with liver dysfunction and gastrointestinal symptoms.
Multicentric Reticulohistiocytosis: This rare disease can cause joint pain and swelling, along with skin lesions and other systemic symptoms. Although rare, it is a potentially treatable condition that should be considered in the differential diagnosis.