Allergies, alone, wouldn't explain dizziness and vomiting. Allergies could affect the inner ear and cause an out-of-balance feeling, similar to what people experience during an episode of motion sickness. There's no allergy that I'm aware of that would directly cause dizziness/vomiting.
You mentioned Meniere's disease, but vertigo isn't always Meniere's. Vertigo is more subject to the coming and going that you describe than most other problems that cause dizziness/vomiting: https://www.webmd.com/brain/vertigo-symptoms-causes-treatment#1 My mom has vertigo - it happens to her just every once in a while, and they haven't been able to find a specific cause.
Is there a reason you suspect allergies?