What happened to my skin? home remedies?

Are there any home remedies for dry skin? what happened to me was I used scar zone on a small acne mark on my chin and I broke out really badly. My fiance bought me "off brand" face cleaning pads because I am Vegan, and they ended up drying out my face and neck so badly that my pores got really tiny and they skin started to peel off on my face, neck and fingers that touched that cleaning pad.

About 3 days went by with this peeling skin ( kind of like when you get a sun burn and it peels off), I haven't seen a doctor because I have no medical insurance and I can't really afford anything since I am in school.

What could have been the problem with that facial cleaner? Did I just experience a chemical peel? any home remedies for dry skin?

PS. most of the dryness and peeling is gone except for my chin/pimple area( which is the area that needed help the most). My hands and neck are completely done peeling and back to normal.