Can mold or allergies be the cause of my niece getting symptoms of tourette syndrome?

No. There' absolutely no evidence that mold allergies, or any other allergy, would cause tourette's. Certainly you may have pulmonary complications from a mold allergy. The belief that an allergic reaction is the cause of development, psychological, or mental health problems is unfounded. This reeks of the belief that an MMR vaccine caused inflammation in the GI tract and lead to autism. Not true!
Yes, AND. Mold and food allergies have been implicated in a variety of health issues from autism spectrum disorder, depression, migraines and even cancer. Bottom line an inflamed GI tract can lead to an inflamed brain (and lungs). Try an elimination diet and see if your niece improves.