The experience you are describing is called
"depersonalization"
A state in which the normal sense of personal identity and reality is lost,
and
"derealization"
The feeling that things in one's surroundings are strange, unreal, or somehow altered
Both "states" are common to anxiety sufferers and they are the result of fatigue. Being tired from being alert "listening in" hour after hour, day by day, waiting for the least little symptom to manifest. Being tired from constantly trying to fight the feelings, dread, anticipation. Stress and worry deplete the body of vitamins and minerals at an alarming rate, faster than cardio exercise. The mind gets fatigued too, from trying to stay on high alert all the time, being tense and constant worrying thoughts and [b]what if[/b] thinking.
Both are harmless, uncomfortable yes, scarey yes, but it just means your battery is low and you need to recharge. When you are feeling this way it is best to just accept it as being fatigued and sensitive, with rest and some nutrition it will go away just like it appeared.