romulus, you should probably post a new thread asking for that advice, as opposed to here. Dating advice stuff from guys is discouraged in girl-gaf because if it's allowed it'll be a deluge of it, with girls in here having to be basically dating advice columnists.
that said, I have some kinda related experience with this. In high school I was way into a girl with Indian ancestry, and I asked her out once. We were great friends for years and had a great chemistry. After I asked her, though, she said she thought I was great but she couldn't. I asked why, and she just said it would be impossible.
I didn't get it at all, but later a mutual friend of ours came up and said, "so you asked [her] out, huh?" I said yeah, and that I didn't get what happened. She said that there's no way her parents would let her be with anybody but another Indian who shared their faith (Hindu in this case). She was close with her parents and would never do anything to mess up that relationship. I was like, but, it's just dating, it's not like we're getting married, and apparently that doesn't even matter, so. It was a rough lesson to learn, and she distanced herself from me afterward, but ultimately the best thing to do is give space and respect her decision. She's under a lot of familial pressure, and I know you feel madly in love with her but it will fade. If she is willing to entertain a guy flying in for an arranged relationship or whatever, then it's pretty much out of the question. The fact that she's hiding your relationship from them says it all.
So ultimately, you're both going to hurt, but trying to keep the dream alive so to speak is going to only make things worse. It's not the advice you want to hear, but what you need to hear. Start accepting it as soon as you can, and give yourself space to breathe and move on. Once you're at the point where you can move on, you can reassess the relationship and see if you can be friends. She may not be able to, or you may not. Just be prepared for that outcome.