If you’re doing this at home, you can distinguish fibres using the burn and bleach tests. Note that it can still be quite difficult to identify the fibres in a blend.
How to tell what the fiber is advises using a 1/2″ square of fabric held in tweezers,and a bunsen burner. I’ve used 6″ lengths of yarn and a Zippo lighter, over a damp cloth.
Use neat bleach in a non-reactive vessel (e.g., glass), and submerge the sample for 24hrs.