Allergies are the result of a mistake by your immune system. It thinks that a perfectly harmless substance is dangerous, and when you encounter that substance your immune system sets off an allergic reaction. Antibodies are released, and they end up triggering a bunch of chemicals that cause your allergic symptoms.
When it comes to house plants, you're more at risk for an allergic reaction if you're allergic to mold than pollen. Often, the soil in potted plants, terrariums, dried flowers and Christmas trees retain moisture and harbor mold. If you're allergic to mold and you breathe it in, you'll end up with an allergic reaction. Pollen allergies are typically a response to airborne particles that grasses, trees and weeds release into the wind to fertilize other plants. Flowers are fertilized by insects, so they -- and most leafy houseplants -- don't release pollen into the air that will trigger your allergies. Some of the few allergenic houseplants to look out for are weeping figs and flowering maples.