Insect bite or sting: This is the most common cause of a bite over the hand, and the symptoms of small dizziness could be due to a mild allergic reaction or anxiety response. Most insect bites are not serious and cause only minor symptoms.

Animal bite (e.g., dog, cat): These bites can occur over the hand and may lead to dizziness due to pain, anxiety, or infection. The risk of infection is higher with animal bites than with insect bites.
Spider bite: Certain spider bites, like those from the brown recluse or black widow, can cause systemic symptoms including dizziness, along with local wound symptoms.

Snake bite: Although less common, a snake bite can cause dizziness among other systemic symptoms due to venom. It's crucial to identify and treat snake bites promptly due to the potential for severe morbidity and mortality.
Tick bite with tick-borne illness: Tick bites can transmit diseases like Lyme disease or Rocky Mountain spotted fever, which can present with a variety of symptoms including dizziness. Early recognition and treatment are vital to prevent long-term complications.
Rabies exposure: If the bite is from an animal that could potentially carry rabies (e.g., bat, raccoon, skunk), it's critical to consider this diagnosis due to the almost invariably fatal outcome if not treated promptly after exposure.

Marine animal bite or sting: For individuals who have recently been in marine environments, bites from certain marine animals (like jellyfish or sea snakes) could cause systemic symptoms including dizziness.
Scorpion sting: In areas where scorpions are common, their stings can cause significant systemic symptoms, including dizziness, especially in children and the elderly.
Severe allergic reaction (anaphylaxis): While not a diagnosis in itself, a severe allergic reaction to any bite or sting could present with dizziness among other symptoms, and is a medical emergency requiring immediate treatment.