Fast breathing and/or shortness of breath can be early or low level anxiety symptoms for some people, so it might not seem like you're anxious yet. The "out of it" feeling, like everything around you is still happening, but you feel like you're in another dimension--if that's what you mean--it's known as depersonalization or disassociation.
That can definitely be an anxiety attack, or in my experience, a panic attack (but you'd know without a shadow of a doubt if that were the case). On the other hand I've had it where it's been like you and seemed to lead to nothing, with athsma specialists stumped, and a full cardiopulmonary workup at the ER coming up with nothing. Monitor your early symptoms. Everybody's different when it comes to the onset of anxiety.