Do not use the ordinary peel if you have sensitive skin. High chances are it would burn and distrupt the skin barrier, because I made the same mistake a week back 😩. Now I have about 4 pimples that won't go away because of the irritation.
I love the Paula's Choice BHA though. It works very well for my skin. Exfoliates without being irritating.
I have also used the Cosrx AHA/BHA but I saw no difference to my skin with that one.
Since you have dry skin perhaps an AHA would work or a combination of both AHA and BHA, if you suffer from clogged pores