Instead of calling your doctor for an appointment, you need to head to an emergency room. While it is true this may be to a sinus infection, it can also be due to an aneurysm. The vomiting and chills are serious. If you read this and have not yet seen a physician, head for the ER.
It sounds like you had an attack of vertigo. I also had similar episodes. It would be best to consult a doctor as vertigo is only a symptom of something else. It can be an ear infection which causes an imbalance, thus the swinging feeling and nausea. But it can also be something else.
In my case, my attacks stopped by itself without any medications. I haven't had any attack for years. Hopefully it has gone.
I would call your doctor for an appt. I have had that before and had a sinus infection and my ears were irratated. Your ears, nose and throat are all intertwined. So you could have an ear or sinus infection or both. Anything that is going on with your ears will cause dizziness and nausea.