Hello,
Triclosan antibacterial face wash contains chlorophenol, a chemical class suspected of causing cancer in humans. Due to this it has been banned in some countries. Since it is causing redness and irritation in your case, so please stop using it. Wash your face with a mild cleanser with moisturizing properties like Cetaphil. Pat your face dry. Then apply a good hypoallergenic moisturizer over the area and see if this improves. If the symptoms still persist then you can apply mild steroid like dermacort.
If the irritation persists then please get it evaluated from a dermatologist.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.
Discard it. It's true what you read about the risk of cancer. The stuff is harsh on the skin, too, which isn't going to be helpful for acne. Those types of soaps also have sodium lauryl sulfate (SLS) in them, as do any commercial toiletry, which another known carcinogen. Skin irritation and redness means the stuff is too harsh for your skin.
Surprisingly, being gentler with your skin helps with acne. I know of a few things you can try: Trader Joe's has a product they sell made by Desert Essence called Thoroughly Clean Face Wash. It's a natural castile soap base with tea trea oil and awapuhi. I don't know anything about awapuhi, but tea tree oil is a natural disinfectant, antibacterial and antifungal. Sometimes even this stuff bothers my sensitive skin, but not always. It is effective on acne.
Okay, now if that doesn't work because it bothers your sensitive skin, then you want to go with something a lot gentler. Natural health stores sell great products for even the most sensitive acne prone skin. One brand I recommend, and I recommend buying it from a discount place, since it's a little on the expensive side, is called Weleda, which is a German company. The boxes and containers are pink, so they do stand out. The one I use when I need something extra gentle is called Almond Cleansing Lotion. This is the one meant for sensitive skin. If you want to try some less expensive products, there are some other natural products that are gentle made by Earth Science. Make sure you get the kind that say fragrance free. The ones with fragrance use natural herbs and such for their source of fragrance, but those irritate my skin. The point is that you don't want to irritate your skin more, since that will actually cause you to break out. Be gentle to your skin and it should clear up.