Infectious Gastroenteritis: This condition is likely due to a viral or bacterial infection that causes both gastrointestinal symptoms (diarrhea, blood in stool) and can be associated with sinus infections if the causative agent affects both the respiratory and gastrointestinal tracts.

Food Poisoning: Similar to infectious gastroenteritis, food poisoning can cause diarrhea and blood in stool. It might not directly relate to a sinus infection but could occur concurrently.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can cause chronic diarrhea and blood in stool. While they might not directly cause sinus infections, patients with IBD can have extraintestinal manifestations, including increased susceptibility to infections.
Diverticulitis: This condition involves inflammation of the diverticula in the digestive tract and can cause diarrhea and blood in stool. It's less directly related to sinus infections but is a common cause of gastrointestinal symptoms in adults.

Invasive Bacterial Infections (e.g., Salmonella, Shigella): These can cause both gastrointestinal and systemic infections, including sinusitis in rare cases, and are critical to diagnose due to their potential for severe complications and antibiotic resistance.
Clostridioides difficile (C. diff) Infection: Especially in patients who have recently used antibiotics, C. diff can cause severe diarrhea and is a critical diagnosis to consider due to its potential for severe complications and specific treatment requirements.
Intestinal Parasites: Certain parasites can cause chronic diarrhea and might be associated with systemic infections, including sinusitis, particularly in immunocompromised patients.

Whipple's Disease: A rare, systemic bacterial infection that can cause diarrhea, weight loss, and joint pain, among other symptoms. It's very rare but can be fatal if not treated.
Eosinophilic Gastroenteritis: A condition characterized by eosinophilic infiltration of the gastrointestinal tract, which can cause diarrhea, abdominal pain, and sometimes blood in stool. It's rare and often associated with atopic diseases or parasitic infections.
Systemic Vasculitides (e.g., Wegener's Granulomatosis): These are rare autoimmune conditions that can affect multiple systems, including the respiratory (causing sinusitis) and gastrointestinal tracts, and are critical to diagnose due to their potential for severe complications and specific treatment requirements.