Not necessarily. Just because you have been taking Xanax (alprazolam) for a week doesn't mean you are addicted. Addiction is when someone becomes depdent on the drug, physically and/or psychologically. When you are addicted, you may develop tolerance to the drug, may require higher and higher doses, withdraw if stopped, and misuse the drug to get the effect you want even if the use is compromising your daily function.
No. Xanax (alprazolam) needs to be taken at much higher dosages, for a much longer period of time, to require weaning due to addiction. I would suggest limiting the dosage to the minimum that is effective, and work on the underlying issues that are causing you to take this medication. You are better off to determine the cause of your anxiety issues, and deal with them with resolution in mind. This is the priority.