Observations appear as thoughts For example when I'm feeling a little anxious, I might think "I'm feeling threatened". These thoughts makes me feel like I am not actually being mindful, because if I actually were then I wouldn't need to think about it, you know? It's kinda hard to explain, but I feel like I'm just fooling myself into believing I'm observing myself, when it's actually all happening within my thoughts.

What's going on here? Am I misunderstanding something?
In my opinion, you are not misunderstanding something. You are being true. 

Many teachers &amp; gurus say thoughts can be observed. I personally disagree here (unless the thoughts are very subtle and very infrequent). 

In my experience, thinking &amp; observing are antagonistic. When the mind thinks, it is not particularly observant. When the mind is truly observant, it rarely thinks.

To genuinely observe anxiety, attention should be drawn to the tremblings or vibrations of the body (the nervous system) and shortness of the breathing. Try to feel the emotion, mood or feeling of anxiety; the pressure in the head (brain) &amp; body, etc. 

That said, it is not easy to do this. If you try, you may need to regularly let go of observing &amp; do some breathing out. The important thing is to trust it is impermanent or a passing mood; like a storm temporarily clouding a clear sky.