Have you tried to redirect her claims back on her? For example, if you were to tell her that your broken arm hurts and she says she understands because UnrelatedXYZ happened to her, try asking her to explain exactly how she could understand JUST because something happened to her. It's easy to make a claim like that, but not so easy to back it up, and making her explain herself when she doesn't make sense might make her consider what she's saying to other people a little bit more.

As for being racist and making everyone else the bad guy, there could be a lot of explanations. There's no excuse for racist, even casual racism, but some people will not change. Again, redirection and turning her words back to her and making her explain them could help this. I had a "friend" (an acquaintance, maybe met him twice) some time ago who was telling a racist joke in a group of people (something about a family tree and hanging) and when he told the punch like, I just looked at him and said, "I don't get it." He was surprised and said, "What don't you get?" I made him tell the joke again to me slowly and I acted super confused the whole time, even though I definitely got it. I asked him to explain exactly why it was funny, and once he got half way through his sentence ("Because, black people were.. lynched.. and.. hung...") he slowed down and got really embarrassed because he realized that he was being especially horrible and not funny.

It may or may not work in every situation, but I find that people with annoying habits like these don't tend to pick up on their own idiosyncrasies until they see them in other people. All it usually takes is calling someone out on being an unreasonable jerk to make them stop. Good luck!