Is my bunny sick or allergic?

If it was allergies, she'd have a small amount of clear discharge. If the "snot" is opaque and white, yellowish, or greenish in color, your rabbit is ill with an upper respiratory infection and should see a vet. This is precisely why it's a bad idea to purchase a rabbit from a pet store. They often have contagious illnesses because of the way in which they are housed and the environments in which they are produced. And the stores care only about their profit, so they lie to sell the animals. Snotty noses in a rabbit are never from "getting used to the new climate" and they don't go away in a few days.