To the OP, I think you are in a position to really change your life, not just your MCAT scores and med school prospects. My mother has been teaching English as a second language for 50 years, so I have some really strong opinions here. Imagine having no language limitations - imagine being funny, eloquent, convincing. Imagine having no hesitation to speak up when you're the only Asian in a room full of loud white guys. Imagine conquering this thing - imagine being able to talk about THAT accomplishment in a med school interview!
You're looking at one crystal clear liability (lack of mastery of English) against a crystal clear and LONG list of assets (GPA, obvious intelligence, immigrant background, persistence). Take away this one liability and there's nothing you can't do. If you go into software, for instance, language skills are the difference between being a decision maker and a decision follower. In medicine, I think language skills are the difference between being the doctor your patients recommend to others, and the doctor whose name people can't remember.
Improving your English means getting off the premed grid. There isn't an academic solution to this problem. Here are 5 ideas, off the top of my head, to dramatically improve your mastery of all the stupid subtleties and exceptions and nuances of English.
1. Live with native English speakers who are quite a bit older than you. Ideally, find an English professor, actor, speech pathologist. Better yet, move to a midwestern city with low immigrant numbers, like St. Paul. Even better: Canada. Get away from the loving arms of your family and friends where it's really comfortable to speak natively when you're tired at the end of the day. (You don't have to give up your Texas residency.)
2. Get a job, any job, where you need to talk to lots of native English speakers all day long. McDonald's is a good example, but you could work at a Kinko's, in a retirement home, at a sports club, at a restaurant, just about anywhere that older born-in-Americans are found. Serve customers who will correct your pronunciation. The less polite your customers, the better. Your actual job at this "job" is to work on your English.
3. Get into theatre. Join an improv group. Do standup comedy. Do an activity where English verbal communication is all there is, a couple nights a week, for a year if you can. A book club would be great, and you'd meet chicks too. By the way, accented perfect English is way sexy - ask anybody.
4. Volunteer at a tutoring center or as a grader, where your focus is reading other people's writing. Learn the intricacies of evaluating writing style and exposition. You'll be amazed how easy it is to judge whether the writer is effective or not. At my school, we have a multicultural center where free tutoring is offered all day long, where you could effectively hang out in the writing center and anybody who wants help will be happy to get YOUR help, even though it's not your strongest subject.
5. Get an English tutor and read one classic English novel per week, or one NY Times editorial page per week. Maybe every two weeks. The tutor can grill you about what you've read, and make you form and justify opinions about what you've read.
So the overall plan that I'd recommend for you is to stop playing premed for one or two years, just to work on your English full time. You can probably support yourself during this time, and you can assume you'll mature and gain confidence and probably have a really good time. Apply to med school again midway through, without retaking the MCAT, because the improvement in your essay and the new story you'll tell may be compelling enough. Then, if necessary, beef up on science again and retake the MCAT. I see this as kind of an Asian immigrant version of the American-born Peace Corps strategy.
I'm in no way trying to imply that English is better, or that this is fair, or anything like that. Your cultural identity is very important, and I'm not suggesting that you abandon or deprioritize it. Mastering English could be the hardest thing you ever do: probably harder than getting into med school, and certainly harder than quitting smoking or losing weight (which Americans typically can't do). It's considerably more difficult to master a 2nd language in adulthood.
But what if you could, and did? Imagine.
Best of luck to you.