Where do fingerprints come from?
By the 17th week of pregnancy, the fingerprints of a fetus are set in stone, observations show. The uniqueness of fingerprints has been recognized for some two millennia and studied scientifically for two centuries (http://www.livescience.com/30-lasting-impression-f...)
Our fingerprints are totally unique, not even identical twins share the same fingerprints! How they form is very interesting and you are spot on, fingerprints develop in the embryo before a baby is born. A person's fingerprints are formed when they are a tiny developing baby in their mother's womb. Pressure on the fingers from the baby touching, and their surroundings create what are called "friction ridges", the faint lines you see on your fingers and toes. These ridges are completely formed by the time a fetus is 6 months old, that's 3 months before the baby is born! (http://scienceline.ucsb.edu/getkey.php?key=2650).
Watch and Learn.