Don't pick. If the skin is flaking off and driving you nuts, you can use a product designed for *lip exfoliation*. Facial stuff will be too harsh. Follow with a pure moisturizer (I've used Neutrogena Norweigian formula hand cream, ok for lips, gentle, not too $$) Let that soak in then top it off with a petroleum lip balm (vaseline lip stuff works great for .99)
L-lysine worked well for me at 1000mg twice a day. The lower doses don't seem to be effective. I added a "stress formula" B-complex (Stresstabs) once a day and I did get my lips back. I had to stay on the lysine for quite a while... almost 6 months before I was able to cut back and eventually stop taking it. (I still take 500mg a few times a week, same with the stresstabs.)
It's not an expensive supplement, definately worth a try. The topical L-lysine balm did nothing for me. Had it not been for my dentist, I never would've tried the pills.