I think that this is an area where your bf needs to take control. You should just step back but be kind when you see her. Even if she is faking, she is upset and acting out as a result. Her behaviour isn't acceptable but it is somewhat understandable.
BF needs to assure her of his love and that your being a part of his life doesn't change that.She needs to understand that you are not a threat but will add to her life and that you made her dad very happy. I would also get BF to get her some therapy and to attend some sessions with her.
Hopefully she will get through this and quit manipulating the situation. If she doesn't get therapy and is allowed to continue pulling her crap, then she will see that as a green light to do it even more in the future. That will obviously be detrimental to your relationship.

Be careful how you explain it to BF as he will be sensitive to her feelings. I wouldn't let on that you think she's faking. Could her passing out be real? My SD12 is very stressed by the divorce and IS passing out and throwing up. The docs say she's having pseudo seizures. It's because her mom makes her keep all kinds of secrets and tells her that if she talks to us about anything that she will lose the kids. BM manipulates her emotions and parentifies her. Her body is now acting out.

I know you feel angry at her but she's still young and she is hurting. You can feel that you don't want her around but if she senses that she will make things worse for you and BF may reject you too. That's his blood and if he's a good dad he will stand by her no matter what!

i went through the same thing with sd19. she was 6 when dh and bm divorced and he didnt date anyone for awhile since he had full custody. when he finally did, sd was throwing temper tantrums and having screaming fits every time his gf was around. he got her into therapy, but she wouldnt cooperate at all, just sat there silently. when i came into the picture, she graduated to chest pains, screaming fits, and panic attacks, totally out of the blue, except coinciding with daddy having a girlfriend again. dh took her to the dr, nothing wrong, except they recommended therapy again. the last time it ever happened, dh and i were going out for dinner and she started in again (she was like 12 or 13 at the time) and i told her we were taking her to the emergency room......suddenly it all went away. we took her anyways, and again, they found nothing wrong and suggested it was psychological. she still refused therapy but she never pulled that again. dh and i tried to talk with her about dh having enough love in his heart for everyone and that no-one is replacing bm, but she was pretty hateful in that conversation as well. i'm so not saying that your sd is or isnt totally faking it, but it IS possible. i always tried to be distant, yet polite to her, and dh never pressured me to be "close" to her. its not an option-she has needed and still needs professional help and now that she's out of state and 19, we cant do much there. many MANY times i wanted to scream my head off at her, and a few times i did, but "killing her with kindness" was never an option for me either. she's incredibly intelligent, manipulative and horribly lazy-she knows exactly what she's doing and she doesnt get kindness from me for that. i feel sorry for her pain, its obvious she still has it, but she also has some SERIOUS boundary issues with bm and i'm just not going to even go there. (ie one of the last times we saw her, sd was on the phone with bm talking about sending naked pics of her boyfriend to bm, and we could hear bm laughing hysterically like that was so cute. its f'd up, is what it is). most of the time, you cant undo what other adults have done, but you CAN demand respect in your own home. i went through hell with this girl and now her brother is starting in too and i'm having to learn this disengaging thing all over again. it never stops. just stand your ground as to what you will and will not accept in your home. bf has to back you up on that too. my dh didnt for a long time, but when he finally did, our relationship got a lot stronger, and suddenly sd started spending more and more time at bm's house, once she realized she couldnt pull her crap at ours. its really hard, and i feel for you...hang in there