Hi Michele:
All anxiety is not routed through depression. Anxiety and depression show themselves differently in the brain (both are difficult to map in the brain because there is no one "anxiety area" and "depression area," but they do tend to involve different patterns of activity in different regions of the brain). Caveat: Anxiety and depression CAN co-occur.
The treatments are also (typically) different. The options for medication are often different, and the options for therapy are often different. Medication and cognitive-behavioural therapy have approximately equal effectiveness for anxiety, although therapy usually produces lifelong results and medication does not (although it can get you through time-limited episodes, of course).
Same for depression: If it is determined that you are experiencing depression, therapy is about equal to medication (mild-to-moderate depression), so you might find that you consider therapy since the medications are causing such unpleasant side effects.
Next question: are the symptoms that you describe signs of anxiety. Possibly. What you have described does not sound like a full-blown panic attack, but you haven't described your full experience, of course (and I am not a trained clinician).
However: could anything else cause these symptoms? Absolutely. For example, too much caffeine (in some people, that's as little as a cup or two of coffee) could cause similar symptoms. A bigger picture might be needed for the source to be pinpointed (for example, a psychologist or physician might ask if you have recognized certain triggers of these symptoms, like every time that you walk into your doctor's office, whenever you are bickering with a friend, etc.).
Major disclaimer here: I am NOT trained in clinical or counselling psychology, the branches that involve delivering therapy.
Reason for disclaimer: I do have a PhD in psychology. My area of research is university student wellness, particularly mood-related factors in alcohol use (I felt anxious, I felt depressed, I wanted to feel some excitement, etc).
