Tom and Rogelio thank you for comments.
Tom,
your post has slightly horrified me
But I think one of my favourite beverages ;-) will help me in fight with potential kidney stones.
But saying seriously I don't think now it is cystine. After your post I've done my own "investigation" in Google resources and I noticed the cystine crystals are quite flat. My crystal is more three-dimensional. It has additional side walls which connect themselves at the top of the crystal. Apart from this I've found the information that such crystals can derive from some pharmaceuticals.
Marek