Stop wearing anything with rayon in it...easier said than done, I know.
You can not get rid of allergies, you can only ease the symptoms.
Are you sure it's the rayon? Could it be the "sizing" chemicals they use in clothes?
Have you been tested?
Take an allergy medication or use an anti-itch cream to soothe the skin.
A Hydrocortisone cream may help the rash, also take a Claritin tablet once a day you can get both OTC..I have found that calamine can also soother as can cold compress on irritated parts..good luck