Confused, Hurt, still Loving Her

Hi, its been almost two months now we broke up with my gf. the whole story started on the internet. we started to talk. she lives in the US i live in Europe. after a few weeks we were texting like 100 times daily, calling each other whenever it was possible when after after 3 months i decided to go to the states to meet her. i went there and we had a wonderful week together. i felt in heaven i didnt want to leave. she was calming me down not to worry as soons as she has the passport she would come after me. it took 3 weeks. She came we moved in together but the happiness lasted only for a few more weeks when she started to drink more and more, she was very distant with me. she had fun with everyone but me, she went out with everyone but me. after a while she didnt even want to get out of the bed. i tried to please her be nice to her do everything she wanted and needed and i got a lot from her but love. when she started to say i am crazy she wants to go home to spend the holidays with her family and friends. within a few days she left saying she doesnt know if she would come back after the holidays. while she was home she broke up with me (so later she could say i didnt cheat on you because we were not together)  we kept talking daily or every second day.. as the returning time was getting closer she became nicer and nicer. she called to tell me to change the date to bring it closer bc she already wants to be home!...here in europe with me. then 2 days before she coming back we were talking and she told me stories what happend to her in those days and she said she is in some girls house (who used to be her gf) i was sure different things happend when finally after denying everything she said yes this and that happend. and that i deserve better so shes not coming back. we talked and talked and agreed she would come back if shes really up to work for our relationship..etc. she arrived with beautiful gift with love in her eyes couldnt even be without me for a few days everything was perfect.. then all the usual thing started again. she was never happy with me. she started to drink. she was nonstop on the net talking to everyone. i asked her to be without the net for atleast a few hours to spend it with me.. to do something to have some fun.. never worked. she kept saying im crazy im jealous but she needs her friends and family. i understand that but still i felt i was nothing at all for her. beside i know trippin over facebook is pretty lame but still she has her life on fb of course i took it seriously. after the first 2-3 weeks she took off that we were in a relationship and never put it back. during the 5 months she never ad a pic of me or of us there... and i wouldnt mind it you know if she wouldnt have kept posting pics of her and my friends together pics of her and different ppl.. everyone but me. it felt very very bad to me it hurt me so much... the last 3-4 weeks together when she already said and knew she was going home again for good this time was horrible. i knew she kept talking to ppl on a more lovely way like how she used to be with me.. i knew she couldnt wait to be home to be with others. she kept telling me no nothing, bc of me she probably do not want any relationship anymore. she hates me im crazy. and as it turned out after 12 hrs flying when she landed a girl (her ex) was waiting for her and she moved in with her they got together again. they were in a relationship posint a million pics together. i was completely lost i felt hurt beyond belief. i was seriously dying i didnt understand WHYYYYY!!! then i went to this psychologist bc by then i couldnt fall asleep for 3 days when she said its not her thing to say anything about this girl but for her it seems she has bpd. she told me to look for it on the net if i want to know more about it...i did and i realized it was true which made it kinda better for me to accept the things, all her words and moveents made sence in that moment. how she was hugging me saying she hates me and when i stroke her hand saying i love her she pushed mine away saying dont lie to me i hate you.. or when she started the scretch my arm with no reason..etc. anyway she told these ppl here in this girl shes with now she can just see the money in her and bc shes  so obsessed with my exgf she lets her do anything just to have her.. still i feel i was used as well she never really loved me. after 3 weeks she left we started to talk again. she said she missed me. when i dont get on aim for a few days, and then i get on she writes me finally ure here i missed you... and when i told her i still have feelings for her she said nothing just to chill. i figured it out she started to have a very similar thing to ours with another girl who lives the other side of the states. now she talkes about moving there. i realized all the little moments we had in this one what they have now and it hurts soooo much. i am very confused why im so in love with a person who lied to me cheated on me used me and still doing it... even if i know she has bpd. why i cant let her go why i cant move on with my life?? please someone tell e what is the best to do bc i know deep inside i do want her in my life bc i care about her, she doesnt know about that she has bpd (sometimes i even doubt if she does or it was just a good excuse for me to accept the happening). ppl told me she has to realize its not my task to tell her...  i dont know what to do, how to be with her. do you think she will find her way back to me too as she did with her exes a million times? even if she does... i doubt i could get into it again..still why i want her in my life?