I've played with skins now for 2 days and still can't get into the Alchemist. When I undress my avatar, it shows the eyesore skin, but nothing shows at the Healer. I've tried removing the skin, but the links are "dead". - Totally frustrated at this point.

I think you can only remove skins in the wardrobe. You can clear current skin in the skin tab, you just have to remember to save before leaving the wardrobe.

If your skin isn't showing at the Healer, I think it probably didn't save properly from the wardrobe. Make sure you click Wear after putting the skin on