Stimulating the Clitoris

I've been married only a few months. I find that my wife has a very unusual reaction when I try to stimulate her clitoris with my hand or finger- basically she doesn't seem to like it. At first, she tolerates it, and seems to get turned on. But after a while she says she feels too sensitive, and pulls away. I've always heard that most women get their orgasms from stimulation of the clitoris, but this doesn't seem to be the case with her. Instead of arousing her, I just seem to irritate her when trying to stimulate her clitoris. What should I do?