Chances for JHU, Duke, Rice, WashU, Princeton, Columbia

Background: Female, Asian, attend a public school that’s fairly decent

SAT: 2270 (690 CR, 780 Math, 800 Writing. I’m afraid a score in the 600s will hurt my chances)

SAT2: 800 Math 2, 690 Bio (will be retaking)

GPA: 4.4/5. School doesn’t rank, but guessing top 3% in my class

Honors classes freshman and sophomore year

Junior" AP Calc BC, AP Bio, APUSH, AP Lang and Comp, Latin (honor-level). Grades all in the A range.
Senior: Multivariable Calc, AP Modern Euro, AP Lit, AP Physics, AP Latin

Awards:
Columbia Book Award
National Latin Exam (silver medals 9, 10, 11)
More Latin crap that isn’t too important

ECs:
Treasurer of TriM (12)
VP of National Honor Society (12)
Captain of Girl’s Varsity Swimming (12)
Varsity Swimming (9, 10, 11, 12)
President of Latin Club (11)
Latin Honor Society (11, 12)
First flute in school ensemble (11)
Youth orchestra (6 years)
Wind quintet (11, 12)
First flute in Principal orchestra (in youth orchestra, 11)
First flute in All-State Festival (11)
NAfME All-National Ensembles flute (12)

Work Experience:
Lifeguard at a lake (10, 11)
Coach for lake swim team (10, 11)

Volunteering:
45 hours at a hospital
Performed at fundraisers and senior homes

Research:
Worked with a professor at a nearby university on a paper with surfactants and EOS. Not sure if the paper will be published when I send my app in…what should I put down in my Common App?

I am going to be applying to engineering (for BME, specifically) schools. I want to be involved in STEM fields. I do know engineering schools have higher requirements, but I’m a girl too…? So I don’t know how that will play out.

Thanks!