Did you take the generic, by any chance? My wife had this same issue when she switched from brand name Wellbutrin to generic. Some will pin this on an anxiety response. Others will suggest it's some of the binders or preservatives in the medications. I can't say for sure, but I can say that my wife has never ever been an anxious person.
Whatever it might be, I suspect it will run its course quickly. If I remember right, my wife's hair stopped falling out about 2 weeks after stopping and then came back to normal after about another month.
Try to do all the things folks normally do to get "toxins" out: drink a lot of clear fluids, exercise, eat a diet high in fiber and whole foods and good fatty acids. Also, my wife found biotin to be very helpful for her hair and nails.