Vertigo/dizziness upon moving head and changing positions for 4 days. nausea and slight headache. just got a cat... does this sound like an allergy?

Vertigo : Not the most likely explanation. Vertigo like you describe is more likely to be due to a viral infection than to your new cat, although it's not impossible for a cat allergy to cause inflammation in your ears and lead to a stopped up head and vertigo. The commonest symptoms of cat allergy are itchy eyes, sneezing, nasal congestion and runny nose. See a doctor soon; vertigo is horrible!