I found an interesting table on telling the difference between various fibers. It also covers the distinction between linen and cotton: http://www.rebeccablood.net/domestic...ent_tests.html
And here is another test: If you have access to a microscope, telling cotton and linen apart is quite easy. Pick a few fibres off a thread and place them under the microscope. Linen has smooth, straight fibres while cotton looks almost wooly. It's a bit like straight vs curly hair. I took this from: http://www.marquise.de/en/themes/howto/stoffkunde.shtml