Yes I think it is possible to be addicted to shopping. If it is having consequences on your life then it is a problem. If you experience obsessions to shop, find it difficult to resist your urges to shop, and find yourself going shopping even when you know you shouldn't/ don't want to, then it's an addiction.

I've experienced this myself. I would promise myself I would stick to a budget I'd set for myself for the week, and then wind up (almost unconsciously) in a shop buying the place up. The pull was enormous. I'm on top of it now, but I have to keep an eye on it. When the obsession is on me to shop, or when I know I am feeling susceptible to shopping I stay away from certain shops. Like an alcoholic who stays away from one drink a day at a time, so too do I stay away from certain shops a day at a time.