Sorry to disagree with some of the posts here - I guess some of these guys are quite experienced Skin Geeks, but I had exactly the same reaction within a week as you a few years back when my beauty therapist at the time switched me to Dermalogica, and she advised I stuck with it.
3 months later it was 10 times worse...by then it had actually become a full blown red rash and I looked considerably older and a lot worse off then when I had started. I got product after product suggested, including finally 'Barrier Repair' the waterless moisturiser for sensitized and damaged skins, to watch my skin keep on getting worse. It cost me a fortune.
I switched back to my original skin care line (which incidentally was Clinique, however I now use Clarins), and within a week my skin had visibly calmed down, the red patches subsided and within a month everything was back to normal.
Please don't think, that I'm knocking the product, as I've come across some real fans of it,
but it obviously doesn't suit some skins and yours may be one of them. I'm sure there's been threads discussing the pro's and con's before. This one shows the differing of opinions - like any range I guess, some love it, some don't.
http://www.salongeek.com/skin-geek/39419-dermalogica-beauty-products.html?highlight=Dermalogica