Viral Upper Respiratory Infection: This is the most common cause of nosebleeds (epistaxis) accompanied by headache, fever, and chills. The inflammation and dryness of the nasal mucosa, along with increased blood flow and pressure during a viral infection, can lead to bleeding.

Sinusitis: An infection of the sinuses can cause headache, fever, chills, and nosebleed due to the inflammation and pressure exerted on the nasal passages.
Allergic Rhinitis: Although less likely to cause fever and chills, severe allergic reactions can lead to significant nasal congestion and dryness, potentially resulting in epistaxis.
Common Cold: Similar to viral upper respiratory infections, the common cold can cause nasal dryness and irritation, leading to nosebleeds.

Meningitis: Although less common, meningitis is a life-threatening condition that can present with headache, fever, and chills. A nosebleed could be a secondary symptom due to increased intracranial pressure or thrombocytopenia associated with severe infection.
Subarachnoid Hemorrhage: A severe headache (often described as "the worst headache of my life") accompanied by fever and chills could indicate a subarachnoid hemorrhage, especially if the nosebleed is profuse or recurrent.
Endocarditis: Infective endocarditis can cause systemic symptoms like fever and chills, and in rare cases, can lead to nosebleeds due to embolic phenomena or vasculitis.

Leukemia: Certain types of leukemia can cause thrombocytopenia, leading to easy bruising and bleeding, including nosebleeds. Systemic symptoms like fever and chills can also be present.
Granulomatosis with Polyangiitis (GPA): A rare autoimmune disorder that can cause inflammation of the blood vessels, leading to nosebleeds, and can also present with systemic symptoms like fever and chills.
Hereditary Hemorrhagic Telangiectasia: A genetic disorder characterized by the formation of abnormal blood vessels, which can lead to recurrent nosebleeds and other systemic symptoms.