What is it called when you're easily awoken up from a dream and you feel intense anxiety and worry?

Nocturnal anxiety: That's usually a form of panic disorder. The first thing to do is to be sure you don't have a medical condition that could cause it. Examples are sleep apnea, gerd, mitral valve prolapse. Assuming you've got a clean bill of health, your doctor might prescribe one of several medications to deal with panic disorder.

Waking with anxiety: From a distressing dream would be called a nightmare & is not unusual. If you have almost no memory of any dream content, just anxiety and dread, it might be a night terror. Those occur in the non-rem period of sleep.