That sounds like a difficult dilemma you are in. As someone who also comes from a multicultural background, I have also felt pressure at times to do what my parents think is best for me. Fortunately, although my family has some traditional values regarding career and having children, they are quite open-minded for Asian parents and have always let me do what I want without too much interference. That is not to say though that their ideas and expectations don't enter affect me and my decision-making.
I think that throughout the years, what I've worked out is that you really have to ask yourself: who are you living for? And if you think you should live to "make your family proud", as you say, why do you feel like you have that obligation?
Personally, I believe there is an important distinction to be drawn between feeling and displaying basic respect and gratitude for our family and all that they have done for us, and living according to their wishes. I think that ultimately as individuals, we have no responsibility to live according to anyone else's expectations except for our own. The other thing to consider is, if you just did what your family wanted but was deeply unhappy, how would that affect the rest of your life (your studies, career, relationship with your family) and ultimately, would that do you and your family more harm or good?
It can be difficult to see things clearly when you are surrounded by different opinions. I would suggest taking some time away if possible, perhaps moving out or going travelling somewhere for a while, and see if that gives you some clarity. Best wishes.