Psoriatic Arthritis (PsA): This condition is characterized by chronic joint pain, skin rash (psoriasis), and inflammation. The presence of elevated inflammatory markers, skin rash with central areas not responsive to topicals, and the combination of joint pain, fatigue, and diarrhea align with the symptoms of PsA. Depression is also common in patients with chronic inflammatory diseases like PsA.

Rheumatoid Arthritis (RA): While RA primarily affects the joints, it can also cause systemic symptoms like fatigue, diarrhea, and depression. The skin rash could be a manifestation of rheumatoid nodules or associated conditions, though it's less typical than in PsA.
Ankylosing Spondylitis (AS): This form of arthritis mainly affects the spine, but it can also cause chronic pain, fatigue, and bowel symptoms like diarrhea. Skin manifestations are less common but can occur.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease and ulcerative colitis can cause chronic diarrhea, fatigue, and joint pain due to associated arthritis. Skin rashes can also occur, and depression is common in patients with IBD.

Lyme Disease: Although less likely, Lyme disease can cause arthritis, fatigue, and neurological symptoms. A skin rash (erythema migrans) is a hallmark of early infection. Missing this diagnosis could lead to significant morbidity if not treated promptly.
Sarcoidosis: This condition can cause inflammation in various parts of the body, leading to symptoms like joint pain, skin rashes, and gastrointestinal issues. It's crucial not to miss sarcoidosis due to its potential to affect multiple organ systems and cause serious complications.
Cancer (e.g., Lymphoma): Certain types of cancer, particularly lymphoma, can present with systemic symptoms like fatigue, weight loss, and skin rashes, along with joint pain due to metastasis or paraneoplastic syndromes. Although rare, missing a diagnosis of cancer could be fatal.

Behçet's Disease: A rare condition characterized by inflammation of the blood vessels, leading to symptoms like joint pain, skin rashes, and gastrointestinal issues. It's less common but should be considered in patients with a combination of these symptoms.
Whipple's Disease: A rare, systemic bacterial infection that can cause joint pain, diarrhea, weight loss, and skin rashes. It's essential to consider Whipple's disease in patients with chronic, unexplained symptoms, as it requires specific antibiotic treatment.
Sjögren's Syndrome: An autoimmune disorder that primarily affects the glands that produce tears and saliva but can also cause joint pain, skin rashes, and other systemic symptoms. It's less likely but should be considered in the differential diagnosis due to its potential to cause significant morbidity if untreated.