Yes, there are some people will be allergic to sunglasses. Some people may be allergic to the component in the plastic or the metal frame, thus their eyes will go red and weep. All sunglasses contain dyes and waxes, which may be the causes, especially for cheap sunglasses.
Some people's skins are so sensitive which will be allergic to the materials of the sunglasses. Some people's eyes will be allergic to the sunglasses because of the inner structure of the eyes. Some eyes may be afraid of the strong lights. However, only few people will have this possibility.