Vasculitis: This condition involves inflammation of the blood vessels and can cause bursting veins. It is a common cause of such symptoms, especially when considering autoimmune or inflammatory conditions.

Hypertension: High blood pressure can lead to the bursting of veins, especially in the hands and feet, due to increased pressure on the vascular walls.
Varicose Veins: While more common in the legs, varicose veins can occur in the hands and may lead to a bursting sensation due to poor circulation and vein wall weakness.
Trauma: Physical injury to the hands or feet can cause veins to burst, leading to the symptoms described.

Deep Vein Thrombosis (DVT): Although DVT typically presents with swelling, pain, and warmth in one leg, it's crucial not to miss this diagnosis due to the risk of pulmonary embolism, which can be life-threatening.
Sepsis: In severe cases, sepsis can cause vascular instability, potentially leading to the bursting of veins. Early recognition and treatment of sepsis are critical.
Disseminated Intravascular Coagulation (DIC): This condition involves both clotting and bleeding and can lead to the bursting of veins due to the consumption of clotting factors and the formation of microthrombi.

Ehlers-Danlos Syndrome: A genetic disorder that affects the body's connective tissue, including the skin, joints, and blood vessels. It can lead to fragile blood vessels that are prone to bursting.
Pseudoxanthoma Elasticum (PXE): A rare genetic disorder that affects the elastic fibers present in the skin, eyes, and cardiovascular system, potentially leading to vascular complications, including bursting veins.
Scurvy: Caused by vitamin C deficiency, scurvy can lead to poor collagen synthesis, affecting blood vessel integrity and potentially causing them to burst.