it is very similar with me and i think its generally common. your brain is trained to produce anxious thoughts, so it does that even when youre not in a particularly frightening situation or when being completely idle. i wouldnt worry about it too much, the techniques are applicable to either type of anxious thinking, doesnt matter what theme they have. this anxiety will shrink as you make progress in your therapy.
what has helped me the most are relaxation techniques / meditation, and activity. any level of activity is helpful, and if you cant get yourself to do large things, do small things.