Edibles or a vaporizer are a good idea to at least not exacerbate the problem while you attempt to find the cause.
How many times would you say you smoked dryer sheets? Did you explain this in detail to poison control?
What is your fluid intake like in a given day? Do you get enough water in your diet, and not too much caffeine or alcohol?
Have you had a doctor take a look at your throat since it started acting up? That would be my very first step if I suspected having smoked a foreign substance. Dryer sheets are made of a plastic-type substance, that does not burn like, say, cotton cloth, and could release very potentially dangerous fumes- not to mention the fragrances.
Please go slap your friend with a rolled up newspaper for suggesting such a foolish thing.