i think you have a right to have anger towards her. but not only her, but also the mental health community that dealt with the both of you. i feel like they should have been better educated to know what DID looks/ed like before just agreeing with what this girl said. further more it is never ok to generalize someones symptoms and say if you don't act like so and so you aren't "sick". i'm sure DID looks different from person to person, not one experience is the same. granted i am no authority on the matter, and i myself do not have DID. these are just my opinions... take them for what they are worth which might not be much.
the one thing i DO KNOW is you have a right to feel angry. id write her a letter (w/o giving it to her) about how you feel about what she's done and how that has made you feel. maybe it will give you closure.