Your adviser is wrong. Colleges don’t know about where else you apply.
Applicants who need a lot of financial aid (like yourself) frequently apply to a lot of colleges because they need their full need met and either colleges don’t or are too highly selective to be predictable.
Applying to more than 8 colleges has nothing to do with “lack of confidence you can’t get into a highly selective college”. It is prudent and strategic when one combines the different factors you have (two schools including one abroad, checkered rigor, high financial need).
Core: if you don’t know what Columbia’s core is, then it’s not for you. Students apply for that… look it up. for highly selective schools “fit” is important.
Try to find a Fiske Guide and/or a Princeton review’s best colleges in your school’s library, and start reading, starting with the colleges listed below.
If your income is 20K, then your application fees are waived (make sure your GC checked it on the commonapp as well as checking it yourself + on SunyApply + CSS Profile) which means you should definitely apply to a more strategic list.
First, you need 2 affordable safeties. Unfortunately, neither Bing nor Stony Brook are safeties for you due to GPA, being more “by numbers” than private colleges (which are holistic), and acceptance rates.
SUNY Geneseo may be a low match so add it as well as another SUNY of your choice (New Paltz, Albany, Oswego…)
Apply to the Honors College or Honors Program at all of these whenever it’s possible (look up Honors College on their website. Sometimes it’s by invitation only but often you have to apply. Honors College = community of motivated, high-achieving peers, special perks, and scholarships.)
Your EFC is zero. You need to find a “Meet 100% need college”. And if you’re premed, you need a collaborative environment with a lot of support to ensure you can rank top 10% in each class you take.
If your family makes $20,000, then you need “meet need” colleges - use your search engine for a list.
It means you’re eligible for the advantage/nudge that is HEOP for NYS applicants, so apply HEOP to private colleges in NYS - please go see your guidance counselor on Monday and ask how you can apply for HEOP. Make that a PRIORITY ie., as soon as you arrive. It’s your best chance at all the top private colleges in your state including Vassar and Cornell, so take it. HEOP criteria usually indicate a GPA or test scores below what is normally expected.
http://heop.org/support/faqs/
CMU: doesn’t meet need, not right for premed, cross out.
NYU: only if you live in NYC and can apply HEOP, otherwise cross out due to poor financial aid.
Cornell: apply HEOP to the contract college CALS - here are the departments of interest to you:
http://ecologyandevolution.cornell.edu/
http://nbb.cornell.edu/
https://mbg.cornell.edu/
(Biology is shared between CALS and A&S, but since you’re a NYS resident you get to apply to CALS while all other students look with envy)
https://admissions.cals.cornell.edu/academics/majors/biological-sciences/
Boston College: are you Catholic? not very nurturing for a premed (competition) AND for a low income student (financial aid is supposed to be 100% but can be dicey, well-known for lack of economic diversity). If the NPC meets full need without loans you’re okay, otherwise cross out.
If you’re Catholic, you may want to look into Fordham (HEOP + they’d be interested in your 33), UScranton,
URochester: good pick, meets 100% need, good for science and premed. Did you apply HEOP? If not, see how you can change it
Add:
SUNY Geneseo (you wouldn’t qualify for HEOP there but they have an additional special “immigrant” factor even for non HEOP applicants; good environment for premeds)
Rice (similar to URochester but in Texas, with “houses” like in Harry Potter), Dickinson (especially like high scores and students who lived abroad, very international - so, very good fit for you), Muhlenberg (very good for premed, early acceptance program to med school), Wheaton MA, Kenyon, Lafayette,Connecticut College, Colby. If you can go a bit further away, Grinnell, St Olaf, Macalester, Rhodes would all be good schools for you to apply to, very strong in the sciences with lots of opportunities for premeds.
St Lawrence (HEOP), Hobart&William Smith, Skidmore (HEOP), Vassar (HEOP) = all very good for premeds, although Vassar would be the most generous financially and the most prestigious; it is actively looking for very low income/high achieving students such as yourself. You definitely need HEOP to have a decent shot at Vassar though.
It may be too late for HEOP so you really need to hurry with that process, contact all the schools.
Apply to Berea College: if admitted, you’re guaranteed a full tuition scholarship and you’ll work every week to pay for room&board. It’s a very good college for students whose families make less than 45K a year.