Light headedness or Dizziness are some common anxiety symptoms. What you can do at that time is sit and do some breathing exercises. It will help you get normal.. Meditation and exercise help me a lot with my anxiety.
You can consult your therapist if needed.
The first thing you should do is get checked out at the doc. If that comes back fine then it would be a good idea to seek out tx with a therapist and psychiatrist if needed. I have experienced the swaying feeling and light headedness and for me it went away with time.
What you are experiencing is a common symptom of anxiety disorder. Sometimes you'll even feel the urge to faint. When you have an anxiety episode and you stated to feel this symptoms make sure that you sit yourself, meditate, and do some breathing exercises. The sitting down is to prevent yourself from fainting, the meditation is to alleviate the anxiety, and the breathing is to prevent a full blown panic attack.
Are you currently under treatment? Yes anxiety is a real inconvenience that if you weren't able to treat immediately can create real damage in your life. Start with your treatments as soon as possible. Don't give up.