one day I was just walking around Solitude when an Altmer working at the radient raiment asked me if I was going to the Blue Palace. As usual I just ignored here and fast traveled to Markarth. For some reason she followed me and asked me the same thing and just walked away. So I just hung around Markarth for a while and fast traveled to Riften and she had followed me there so I decided she was a Thalmor spy and led her to Gallows Rock where I got rid of her. Has anyone else experianced glitchs like this.

nope.

I know NPC's will follow you through a 'cell' door when you move through one and they are talking to you, but I havent heard of one following you that far.
Also, she was asking because she has a misc quest for you to show off some of their clothes to the Jarl, or something like that. A _{very arrogant} seamstriss and nothing more.