You seem really lost about what you should do. I'm a little confused about your letter, so just bear with me while I briefly run through it.
You've met a guy whom you're very much in love with and he cares for you. The two of you want to have a relationship. Your parents are dead against this and are very upset. You don't want to end this relationship. You're afraid of whether you could ever love another because your feelings for your current love may linger.
What should you do?
Take some time out and ask yourself these questions:
Are You Prepared To End It?
Leaving aside your parents' dictates and whether or not there is a future to this relationship, do YOU want to pursue this relationship? To me, you come across as a girl who has been obedient all her life, and it seems your parents are keen on ultimatums, if you want to pursue your relationship while trying to reason with them, are you prepared to go against their ultimatum to end it?
If you pursue this relationship, how do you think your parents will react? Imagine telling them that you want to go ahead with this, but want their consent even if it will take a while, how will they react? What can you do to gently settle everything while maintaining your stand?
What will your parents do to prevent you from pursuing this relationship? What can you do to prevent this?
Does Your Boyfriend Know the Consequences?
Does your "boyfriend" know that the consequences for you are far greater than for him? Is HE prepared to go ahead with this? I know the two of you are committed to each other, but this is a serious decision and have you spoken of the details of everything that may flow from wanting to stay together?
None of us can predict whether there will be a future to this relationship. But this is a very big step and you need to ask yourself whether all this is worthwhile FOR YOU.
I can appreciate the difficulty you are in. On the one hand, you would want to enjoy this relationship, but on the other, and quite rightly, you're afraid of the consequences. From your letter you seem very ambivalent about what you should do, but reading between the lines it seems you would be keen to pursue this relationship while quietly appealing to your parents to see that what you value most is their blessing.
Are you Prepared To Be Ostracised?
I really can't ask you to do what pleases you, because I can understand that Asian culture is bound by what the majority dictates and it's very difficult and unpleasant to run against this. You need to ask yourself what would make you happy.
If you know that, in time, your parents will come round (but it will take a while), and you are prepared to go through all the pressures of going against their (and your) community's wishes (you may have to get a place of your own, subsist on your own income, and put up with being ostracised and vilified by most), then I would advise you to go ahead with it.
Your Father Shouldn't Emotionally Blackmail You
In my experience, even the most stubborn can be brought round to see reason, you just need to find the right way to communicate. I can understand that your parents will be unhappy, and like you, agree that they will eventually come round to accepting your choice; my biggest fear is for the health of your father. To me, there is an element of emotional black mail here, and he cannot use his health as an obstacle to your peace of mind and happiness.
That said, you need to be very delicate and gentle here, pre-empting all the pitfalls and making it as easy as possible for your parents to bear.
Seek the Counsel of Someone Who Knows You
It might help to seek the counsel of someone who knows you well and wants what's best for you. That way you could get an objective perspective on what you should do.
Wish you the best of luck.