Hi, I'd like to help you with your question.
Although fatigue, lightheadedness and overall malaise can be symptoms of anxiety, it is not usually all the person feels.
You are correct, anxiety usually manifests itself with racing heart, nervousness or feeling edgy, sweating, the need to get out of where ever you are, trouble concentrating, and sleep difficulties. And these are only some of the possible symptoms. In my experience, most people with anxiety present with more symptoms than you have and are not sure what they have. They may mentioned feeling physically bad, but mostly they talk about how they feel rather than feeling sick physically.
There are many forms of anxiety. But your symptoms, though part of anxiety, do not seem to fit the normal presentation of anxiety symptoms. If anything, it sounds more like depression than anxiety, if you are looking at a possible mental health cause. But even then, you would not describe feeling sick as much as you would say you feel down or sad.
Has your doctor ruled out Epstein Barr or Chronic Fatigue Syndrome? Although I am not a physician, your symptoms remind me of those disorders.
Did your therapist do an evaluation? This would either tell you if you fit the criteria for anxiety or depression or it would rule it out. Your therapist should have been able to tell you if you do have either anxiety or depression.
You also may want to switch doctors and get a second opinion. Doctors can be wrong, like anyone else can, and it helps to have a new perspective on your situation.
I hope this helps,