I have a wort, and I place cream on and around it. The cream causes the skin around the wort to peel off. The peeled skin is basically off, but it just needs one pull to rip it off. Is it permitted to rip off the dry skin on Shabbos. And furthermore, what is the rule with scratching off dandruff on Shabbos, or a little piece of skin that sticks out after cutting your nails?

No, one cannot rip off skin or dandruff on Shabbat.