The plants might be a concern, as a direct source of potential
allergensAllergen
Positive reaction to allergen and secondarily due to
fungiFungi-guard
Fungi-nail that often grow on plants. And then there might be problems from fertilizers or plant foods, and pesticides.
Even with that being the case, placement of the plants in parts of the house less frequented by your child; definitely not in your bedroom or the child’s, the removal of drapes and carpets that might hold and release plant pollens and not vacuuming when your child is near or, ideally, for at least 1 hour thereafter.
Your best source of information would be a board certified allergist who might be able to recommend plants, less likely to be a problem for an allergic person with asthma. To learn more please read our asthma information by copying and pasting this address
http://www.nationaljewish.org/disease-info/diseases/asthma/index.aspx
into the address window of your internet browser.