The result of peels is often dependent on your purpose of going for that peel. Some may show immediate visible results, while others may wait till the redness goes away and the new skin cells are there.
It takes around 2-3 weeks for the new skin cells to form and start functioning. The full results of peel are usually visible after the full healing of skin layers occurs. It will take longer for you to see the results after a medium or deep chemical peel.