Financial aid is need based, with need determined based on the financial aid application that your parents fill out (due February?)
Unlike colleges, most prep schools are not need-blind in acceptances. If a school likes you, but has already allotted all their financial aid to applicants they really really like, you will be waitlisted. So, if you need a lot of financial aid - say, over 90%, it can be a crap shoot.
If admissions thinks you’re really amazing, they’ll find the $. But if you aren’t viewed as a super asset in some area where they have a need, then you are a lower priority. What each school sees as a “need” varies from year to year.
You have the added problem that you are applying to enter as a junior. There are fewer openings there. Would you consider applying as a sophomore repeat?