L-optizinc is a really good one to use (zinc methionine), and you can use zinc oxide cream (nappy rash cream) to test your reaction to it. If you've got really thin skin, that stuff will get absorbed up right damn quick!
Be aware that copper is a cofactor of zinc, and it's best to go after a supplement that combines them. (I use a jarrow formulas one myself). Copper is important in collagenic tissues (like skin).