I think what you are referring to is called "rumination".

http://en.wikipedia.org/wiki/Rumination_(psychology)

I do it all the time so I know how you feel! I don't know what your other symptoms are (and I am obviously not a professional) so I can't say whether you have an anxiety disorder or not. Ruminating can be symptom of a number of mental health conditions or maybe just a personality trait kicked into over-drive.