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Yes that is entirely possible - especially if you are breaking out when you don't normally. If you are not breaking out and your skin is just getting red when it usually doesn't, then it might be more likely that the products you are using are irritating your skin and may be too strong. You did not mention exfoliating but if you are using any kind of face scrub that can definitely cause redness as well and, in that case, should only be used once or twice per week.
If you give it a week and you find it is getting worse and not improving at all, you might want to discontinue using those products. It could just be one of the products that is causing the redness. Toners can be especially irritating so trying just your cleanser and moisturizer without the toner might help as well.
But a sign that it is pulling the impurities out of your skin is usually when you have breakouts which might also have some redness. But if you are seeing only redness, it is much more likely that you need products for more sensitive skin.
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