Apart from allergy to the metals in orthodontic appliances, other reported allergic reactions are linked to latex products and polymers. Latex is found in most elastic ties for braces, as well as in the intermaxillary elastics used to correct the bite. Of course, there are latex-free elastics, and these can be used if you have an allergy.
Polymers are a group of plastic materials, and the material aligners are made from belongs to this group.
An allergic reaction to aligners may be suspected if you have the following symptoms: a rash and redness of the lining of the mouth, a rash and redness of the skin of the face, most often around the mouth, swelling of the tongue or lips, a burning sensation in the mouth, and changes in taste and other sensations. If such reactions occur, treatment should be stopped and the appliance replaced after consulting an allergist.
This answer is for general information. Your own case needs an examination by an orthodontist.