Hi emily,
i've suffered from the same thing for about 8 weeks now. It's not like i'm going to faint or feel nausea, but sometimes I feel like my eyes go out of place and my legs are weak. It's not disabling, but it's certainly uncomfortable.
It happened when I had a stress breakdown over a diagnosis. Fortunately I was fine. Emotionally I was not able to handle so much stress, so I kind of collapsed. I had attacks of anxiety that provoked extreme fatigue, depression and the dizziness you describe.
But I can say that I am recovering slowly. A month ago, the symptoms were much worse. I decided to go to a natural health doctor, and he put me on a nutritional treatment. It has helped me wonders with my fatigue (now down about 70%), my anxiety and stress.
My recommendation: find a place that offers neuromuscular therapy... It consists on pressing on certain trigger points on your body and it's amazing for stress, anxiety, tension, muscular pain and similar. I know it has worked for me. I've had three sessions already, still three more to go.
Not everyone responds the same to treatments, but based on my experience I believe it can help you feel much better.