The symptoms you describe are just derealization-type symptoms. They are harmless. Some people feel detached from their self, some people feel unreal, some people describe it as dizziness or vertigo. If you take a moment and soften your grip on yourself you'll probably notice your scalp muscles have been tensed, or if you're particularly anxious, the tension will be swimming instead of fixed. Either way, the bottom line is that you are now holding tension in your head which causes these kinds of symptoms.
As mentioned above, the quickest route to recovery is by coming to a genuine understanding and belief that it is all harmless anxiety, which doesn't feel harmless, and is very uncomfortable, but is actually harmless. Once you have this understanding, you must next realize for yourself that the more you try to make it go away, the more you reinforce it and keep it alive. Staying engaged is fine, but don't fearfully and hastily try to find things to keep your mind occupied just to escape it - this will just bury it and it will probably eventually come back. Calm and steady engagement in activities is good. This all embodies the attitude of acceptance.