Postural Orthostatic Tachycardia Syndrome (POTS): This condition is characterized by a rapid increase in heart rate and other symptoms that occur upon standing, which can be triggered by a viral illness like measles. The recent history of measles and the symptoms of dizziness upon standing make POTS a plausible diagnosis.

Vasovagal Syncope: This is a common cause of fainting spells in children, often triggered by standing for long periods, stress, or illness. The symptoms can include dizziness, nausea, and fainting, which might align with the patient's complaints.
Anxiety or Panic Disorder: Anxiety can cause dizziness, especially in children who have recently experienced a significant illness. The nasal congestion could be unrelated or a focus of anxiety.
Dehydration or Electrolyte Imbalance: Following a viral illness, dehydration or electrolyte imbalances can occur, leading to symptoms of dizziness when standing.

Intracranial Hypotension: Although rare, this condition can cause dizziness and is a potential complication of a lumbar puncture or, in some cases, a viral infection. It's crucial to consider due to its serious implications.
Subacute Bacterial Endocarditis: This is a rare but serious condition that can follow a viral illness, especially in individuals with pre-existing heart conditions. Symptoms can be non-specific, including dizziness.
Neurological Complications of Measles: Measles can lead to serious neurological complications, including encephalitis and subacute sclerosing panencephalitis, though these are rare.

Chiari Malformation: A structural defect in the cerebellum that can cause dizziness among other symptoms. It's a rare condition but could be considered if other diagnoses are ruled out.
Mitochondrial Disorders: These are a group of disorders that can affect many systems in the body, including the nervous system, and might cause dizziness. They are rare and would typically present with a broader range of symptoms.