If my mom has anxiety disorder, am I more likely to get it too?

Perhaps, in two ways. Genetics plays a role in depression with more than expected frequency in specific families. It could be a genetic predisposition but there is the distinct possibility that some of the anxiety found is a learned response from being around a family member who deals with stress by being anxious. It would be hard to tell the difference since there are no clear studies that have tried to separate them.
You're in control. While panic attacks may be physiological, chronic anxiety is often about dysfunctional learned patterns of thinking. Especially with some guidance, you can learn to reprogram these, even if you grew up in a home full of worriers, insecurity and drama.