Is there such thing as allergies to rayon?

Answer 1

Not only 'yes', but 'hell, yes'.

Rayon is not 'synthetic' (made from chemicals). It's 'man-made' -- made from anything they can fit into the pot. Usually, this means various forms of cellulose, but since the underlying materials come from nature, it's only too possible for people to have allergic reactions. Worse, since it's pretty near impossible to know exactly what went into the pot (wood chips? kudzu? seaweed?), the potential allergic reaction is completely unpredictable.

All natural products have the potential to cause reactions in sensitive people. Rayon has a low incidence of allergic response, but it's not zero. Polyester is a synthetic: no organic components. Rayon is not.

However, if you have a bad reaction to one rayon product, you won't necessarily have any reaction at all to another. The underlying materials that went into the manufacture of the fiber vary. The best you can do is, first, recognize that the allergy is real; and second, try things out and see if a given item causes a problem.