I posted the exact same thing a few weeks ago and people gave me some good advice. You might want to look up that thread. I think it has the word "Fingerpicking" in the title.

I could play for hours without any kind of pain or fatigue as long as I was strumming, and then as soon as I started working on fingerpicking, ouchie ouchie, after just a few minutes, my fret fingertips, wrist, everything hurt like I was a raw beginner again. It was suggested to me (and the people on that thread will say it better than I'm paraphrasing) that I was tensing up without realizing it because I was learning a new skill, and that, in my experience, was indeed the case.

In other words, practice will fix it. In the meantime, a Musician's Practice Glove comes in handy in times like that.