I feel so bad

[mosaic]

that is really a dilemma. i don't know what i would do either.

is the friend request for the DID group or for you personally? if it is personally, are you interested in having her as a friend on Facebook? if not, you don't have to accept the request. and if you are interested, and accept the request, if she ever brings up the topic of the mutual friend you can politely say you don't talk about other people (forget mentioning diagnoses unless she brings it up).

that's how i am seeing it right now. unfortunately, things are usually a lot more complicated than what you can provide in a post here, and this approach may not be appropriate. as MDs used to say, YMMV.