I've a somewhat interesting take on this from experience. I'm an ex-mormon who dated a jack-mormon for years. The problem in our relationship was a whole web of secrecy. Her parents were devout LDS members who put a lot of their feelings into their faith. (She actually doesn't believe in the faith, but pretends she does to this day because she doesn't want kicked out of the house. Cheaper than an apartment.) With that, her parents didn't take kindly to their daughter getting in a relationship with a non-mormon because they 'knew' there was no chance of a long-term relationship. As such, we had to keep it off the radar from practically everyone because we didn't want it to get back to her parents in some form or another. We dated other folks to try to keep up the appearance that we weren't together. That was a compromise that worked for her parents, knowing that she wasn't
really interested in me, because she dated other folks. We continued this approach at a relationship for four years until the transition from high-school to college and we went our separate ways. (An unpleasant breakup caused by a litany of factors including the secrecy, but ultimately unrelated to your predicament.)
What I'm going to say here and now is
do not go the route I did. It's not worth keeping things like this a secret from her parents. What you need to do now is figure out whether this is a relationship you want to pursue in the long term. If this is, you need to stop the charade you're playing with her parents and be honest with them. If you can't respect her parents enough for them to know the truth of your feelings, who you are, and your intentions, why should they trust you with their daughter?
If in the future this relationship
did work out, how do you think her parents would feel about you once you did spring it on them you two were going behind their backs the entire time? You two have created the same idealized fantasy that I did, that all you need is each other. That's not true, and it's a very unhealthy relationship to be in, especially in the younger years.
The best thing you can do to get this relationship to work is try to talk with her parents. If you are open and honest with them, I'm sure that will earn you some points in their book. I can't guarantee that they'll respect you enough that they'll approve your relationship, but it's really the only way you've got. If it works out, they approve of a relationship between you two, and you two go on your merry way of dating that's fantastic. But this ultimately leads to 'the big question.'
Should you really continue a romantic relationship with this girl? I know that right now you probably are thinking she's the only one for you, that she is your world. I bet it's hard for you to imagine that you could possibly love anyone else. But something you need to remember is that long lasting relationships formed in high school are the exception, not the rule. There are a couple difficult questions you need to ask yourself, even if painful.
The first is - did she really break up with you because of her parents? When people break-up with others, they don't want to hurt the other person. They'll often attribute it to other factors and try to console you with the implications of hope for a future together. This approach is completely wrong, but still often used. The reason I want you to ask yourself this is she's probably gearing up to go to college. (I assume she's a Junior) She may be evaluating herself, her goals, and her dreams and might have come to realize that the
romantic feelings she felt for you are just absent. So she might have tried to create a scapegoat to let you go easily and not resent her. You should find out first if she really does want the relationship to continue, or if it really is her parents.
The second is - assuming she
does still have feelings for you and considering the secrecy you've created, should you really continue this relationship? (It's not a question of 'wanting it to continue,' you obviously do. It's if you
should continue it.) Her parents might end up approving your relationship, but that doesn't change the fact that your relationship's very existence was predicated on a web of lies. In my experience, I thought I'd be fine with it. But in retro-spect I realize that my lies and secrecy doomed my relationship from the get-go and I would not have been comfortable with it. Remember, in Romeo and Juliet those two
die because of the secrets.
With that, it leads to a final question you should ask yourself - is this an opportunity in disguise? You have learned a lot from your relationship with this girl. Maybe now would be the perfect time to throw in the towel. Forcing a relationship to work, especially in high school, is not a good idea. You two aren't married, and there aren't kids involved. There is nothing to say you two need to be together except for the feelings in your heart, and trust me, those can change. You can use this experience as an opportunity to start a new, healthier, and less complicated relationship (given time to move-on) with someone.
Regardless of whether you choose to pursue this relationship or not, remember one thing: you always have yourself. It feels like you've given every bit of yourself to this girl, but in the end you're still
you. You shouldn't have to sacrifice yourself to make a relationship work. A healthy relationship, while it will inevitably have its good times and bad times, ultimately results in you finding a person who complements you. Someone who makes you stronger. It's not selfish to end a relationship for your own needs. Even if it doesn't work out between you two, it doesn't mean that you're bad or that she's bad. What it means is that it didn't work out.