Yes, you can have GAD (generalized anxiety disorder) and panic disorder at the same time. Anxiety disorders are highly comorbid with each other, meaning different anxiety disorders can occur at the same time.
The defining characteristics for GAD is excessive worrying about everyday events, restlessness, low energy, muscle tension, sleep disturbance, irritability, and poor concentration. And these symptoms for GAD are chronic, and last most of the day, most days of the week.
Panic disorder is marked by discrete episodes of panic attacks. You also have anticipatory anxiety from waiting for the next panic attack to occur. With panic disorder, you may also develop agoraphobia, which is a fear of having a panic attack and not being able to get help or to escape while away from home.