Hey Legi I went through similiar thoughts after this April test. I scored:
6VR 10BS 11BS this April and decided to apply. I've thus far recieved SCREENED secondaries from schools like UCSD, UC Davis and Michigan State. My letters of rec only recently went out a couple days ago so I can't expect to hear from schools for anyother few weeks.
In any case, though I was born in Los Angeles, I was raised in a Spanish-Speaking home and attended LAUSD schools my entire life. I feel the sole fact of recieving my education from a school district that made headlines for producing the lowest national test scores in the nation should lend support to my DRIVE to succeed and may help explain a 6VR. I think if you have a reasonable explanation (and I think you do since you're ESL) then you should apply.
I am sure there are schools out there that are not so narrow-minded to deny an otherwise motivated and intelligent student the wish to help people with thier health problems. If your application is solid: double digits in the sciences, 3.5 or higher gpa, health-related experiences and some extra-currics that may stand out then apply. all you need is one school to give you a shot.