Linen is made from plant fiber, and burning it will turn it to ash with a slight wood odor when burned. Synthetic fibers will melt and form a blob. There is also a distinct texture and weight to pure linen.
Sometimes a stain can come out just by soaking or letting it fade, depending on the stain and the material. Check to see if your curtains can get wet, and...
Use witch hazel afterward to help alleviate the burning sensation. Next time you shave, mix the olive oil with another oil to tone it down in case you are allergic...