Both PE and cotton produce CO2, but they distinctly have different smells while being burnt (Burning PE has smell of candle wax, while burning cotton’s smell is like burning leaves). Wool produces CO2 and N2 which is odorless, but yet has smell of hair burnt. Moreover, they also differ in burning process (PE and wool burns slowly, while cotton burns rapidly). So why there are such differences when their products are similar?
What are your burning conditions? PE fibers are indeed only carbon and hydrogen. But don't forget that wool is a protein (main component keratin) fiber and does not only contain carbon, oxygen and hydrogen, but also sulpher. That will also have an influence on your smell ;) Whereas cotton is pure cellulose, if you do not have any waxes remaining.