Chlorine Gas Poisoning: This is the most likely diagnosis given the patient's recent exposure to chlorine fumes from the hot tub. Chlorine gas can cause severe irritation to the eyes, skin, and respiratory tract, leading to symptoms such as dizziness, nausea, and eye burning, which the patient is experiencing.

Acute Respiratory Distress: Inhalation of chlorine fumes can lead to inflammation and damage to the lungs, causing respiratory distress. The patient's symptoms of dizziness and nausea could be indicative of hypoxia or respiratory compromise.
Chemical Burns to the Eyes and Skin: Direct exposure to chlorine gas can cause chemical burns to the eyes and skin, leading to pain, redness, and a burning sensation, consistent with the patient's complaint of eye burning.
Anxiety or Panic Attack: The traumatic experience of inhaling toxic fumes could trigger an anxiety or panic attack, characterized by shakiness, dizziness, and nausea.

Pulmonary Edema: Although less likely, chlorine gas exposure can lead to pulmonary edema, a potentially life-threatening condition. It is crucial to monitor the patient's respiratory status closely.
Cardiac Complications: Chlorine gas exposure can also affect the heart, leading to arrhythmias or other cardiac complications, especially in patients with pre-existing heart conditions.

Chlorine-Induced Asthma: Some individuals may develop asthma-like symptoms after exposure to chlorine gas, although this is less common.
Other Systemic Effects: Rarely, chlorine gas poisoning can lead to systemic effects such as kidney damage or neurological impairment, although these would be expected to present with more severe initial symptoms.