You can be allergic to the chemicals or plastics used in the manufacture of some fake trees. Symptoms can include skin irritation, respiratory problems, and even anaphylaxis in severe cases. However, there are also some hypoallergenic fake trees available, which are designed to reduce the risk of allergic reactions. If you think you may be allergic to your fake tree, it's best to check with a doctor or allergist to confirm the cause of your symptoms and explore possible solutions.