Is it okay for oily & acne prone skin to suddenly get dry with a anti-blemish soap? (See description please x)

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I started using the body shop tea tree line a week ago and at the beginning my skin remained normal after the wash and it started clearing up. Now, after each wash, my skin feels tight and starts flaking at certain areas. I thought that that may be the dead skin being gradually removed from my face, and if that is what it is then it sounds good. I do wash my face with that tea tree soap 2-3 times a day, I have used the tea tree scrub 3 times up to now and after every singe wash I use pure tea tree oil on my face. I don’t apply any moisturizer and I anyway didn’t use one before using these products because my skin used to get very greasy with it. Any ideas? Does it work like that?

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