Its a dissociative disorder. One of the most common problems in anxiety sufferers. So if you have problems with anxiety and panic, and you are having the symptoms you are, they are caused by the anxiety.
Depersonalization and Derealization specifically are what they're called. They do extend long after panic and anxiety stop. Actually the annoying part is they keep going until you distract yourself from them. But it feels so weird that how can you not pay attention?
But yeah. you can look the terms up on Wikipedia if you like. They'll basically be a list of tthe symptoms you described though. If it helps, a lot of us really do have these problems, and it does get better once you accept its not dangerous.
For a short term fix, the next time you're feeling this way, look at this picture: http://i611.photobucket.com/albums/tt194/kamrom/sqsis.jpg
It's so distracting to your brain that your feelings of dissociation vanish rapidly.